Aug 27th
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The document discusses an algebra lesson that took place on August 28th. The learning outcome was to use deductive reasoning in proving algebraic properties. Students worked on simplifying algebraic expressions like 5(2n+3)-7 and 6(n+5) - 9^2. They also completed classwork problems from page 54, numbers 3 through 5 of their textbook.
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Aug 28th
This document outlines an algebra lesson where students will use deductive reasoning to prove algebraic properties. The lesson includes simplifying expressions as a warmup, then working on problems from the textbook involving finding patterns in tables to relate terms involving n to Sn and Sn+1-Sn.
Graph Coloring
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Scheduling Final Exams
Frequency Assignment
Index Registers
November 18, 2015
Today's tasks include:
1) Practicing the last Khan Academy topic for the week on literal equations
2) Focusing on solving literal equations for a specified variable
3) Making significant progress on Classwork 2.3, which is due November 18th and involves solving various equations for unknown variables.
2.4 derivations and languages
This document discusses derivations and languages in context-free grammars. It covers recursive inference versus derivation to determine if a string belongs to a language. It also discusses leftmost and rightmost derivations, derivation trees, sentential forms, and left and right recursive grammars. Several example problems are provided to demonstrate derivations, parse trees, and generating strings from given grammars.
Hard times to come
Hard times to come. There are not simple groups of order 2016. The document then provides a proof by contradiction. It analyzes the possible values that the number of Sylow 7-subgroups could take and shows each leads to a contradiction. It concludes that a simple group of order 2016 does not exist.
2.5 ambiguity in context free grammars
The document discusses ambiguity in context-free grammars. It provides examples of ambiguous grammars, including one where the grammar G with production rules X → X+X | X*X |X|a is shown to be ambiguous because the string "a+a*a" has two different leftmost derivation trees. It then lists four other grammars and briefly states that each one is ambiguous without showing the derivations.
Coloring graphs
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.
Recommended
Aug 28th
This document outlines an algebra lesson where students will use deductive reasoning to prove algebraic properties. The lesson includes simplifying expressions as a warmup, then working on problems from the textbook involving finding patterns in tables to relate terms involving n to Sn and Sn+1-Sn.
Graph Coloring
Graph Coloring
Chromatic Number
Application of Graph Coloring
Scheduling Final Exams
Frequency Assignment
Index Registers
November 18, 2015
Today's tasks include:
1) Practicing the last Khan Academy topic for the week on literal equations
2) Focusing on solving literal equations for a specified variable
3) Making significant progress on Classwork 2.3, which is due November 18th and involves solving various equations for unknown variables.
2.4 derivations and languages
This document discusses derivations and languages in context-free grammars. It covers recursive inference versus derivation to determine if a string belongs to a language. It also discusses leftmost and rightmost derivations, derivation trees, sentential forms, and left and right recursive grammars. Several example problems are provided to demonstrate derivations, parse trees, and generating strings from given grammars.
Hard times to come
Hard times to come. There are not simple groups of order 2016. The document then provides a proof by contradiction. It analyzes the possible values that the number of Sylow 7-subgroups could take and shows each leads to a contradiction. It concludes that a simple group of order 2016 does not exist.
2.5 ambiguity in context free grammars
The document discusses ambiguity in context-free grammars. It provides examples of ambiguous grammars, including one where the grammar G with production rules X → X+X | X*X |X|a is shown to be ambiguous because the string "a+a*a" has two different leftmost derivation trees. It then lists four other grammars and briefly states that each one is ambiguous without showing the derivations.
Coloring graphs
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.
Graph colouring
This document discusses graph coloring, which involves assigning colors to the vertices of a graph such that no two adjacent vertices have the same color. It provides examples of problems that can be modeled as graph coloring, such as scheduling committee meetings. The key points covered include defining graph coloring and chromatic number, discussing greedy algorithms and their limitations for graph coloring, and presenting the Welsh-Powell algorithm as an approach to graph coloring.
Graph coloring and_applications
Graph coloring involves assigning colors to objects in a graph subject to constraints. Vertex coloring assigns colors to vertices such that no adjacent vertices share the same color. The chromatic number is the minimum number of colors needed. Graph coloring has applications in scheduling, frequency assignment, and register allocation. Register allocation with chordal graphs can be done in polynomial time rather than NP-complete, since programs in SSA form have chordal interference graphs. A greedy algorithm can color chordal graphs in linear time, enabling simple and optimal register allocation.
Edge Coloring & K-tuple coloring
This document discusses edge coloring and k-tuple coloring in graph theory and computer applications. It defines edge coloring as assigning colors to edges so that edges incident to a common vertex have different colors. The minimum number of colors needed is the edge chromatic number. It also defines k-tuple coloring as assigning a set of k colors to each vertex such that no two adjacent vertices share a color, with Xk(G) being the minimum number of colors needed. An example shows C4 requires at least 4 colors for 2-tuple coloring.
Graph coloring problem
The document discusses graph coloring and its applications. It defines graph coloring as assigning colors to graph vertices such that no adjacent vertices have the same color. It also discusses the four color theorem, which states that any planar map can be colored with four or fewer colors. Finally, it provides an overview of backtracking as an algorithmic approach for solving graph coloring problems.
Bipartite graph
This document discusses graph coloring and bipartite graphs. It defines a bipartite graph as one whose nodes can be partitioned into two sets such that no two nodes within the same set are adjacent. Bipartite graphs can be colored with two colors by coloring all nodes in one set one color and nodes in the other set the other color. The four color theorem states that any separation of a plane into contiguous regions can be colored with no more than four colors such that no two adjacent regions have the same color. Applications of graph coloring include exam scheduling, radio frequency assignment, register allocation, map coloring, and Sudoku puzzles.
Graph coloring using backtracking
This document summarizes graph coloring using backtracking. It defines graph coloring as minimizing the number of colors used to color a graph. The chromatic number is the fewest colors needed. Graph coloring is NP-complete. The document outlines a backtracking algorithm that tries assigning colors to vertices, checks if the assignment is valid (no adjacent vertices have the same color), and backtracks if not. It provides pseudocode for the algorithm and lists applications like scheduling, Sudoku, and map coloring.
GRAPH COLORING AND ITS APPLICATIONS
Graph Coloring and Its applications
Project for HERITAGE INSTITUTE OF TECHNOLOGY
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This document summarizes a presentation on graph coloring. Graph coloring involves assigning colors to the vertices of a graph such that no two adjacent vertices have the same color. It has applications in problems like channel assignment. The document defines key terms like k-coloring, chromatic number, and k-chromatic graphs. It also discusses the NP-complete nature of the graph coloring problem and summarizes basic greedy and Welsh-Powell algorithms for graph coloring.
Graph coloring
This document presents information about graph coloring. It defines graph coloring as assigning colors to the vertices of a graph so that no adjacent vertices have the same color. There are two types: edge coloring and vertex coloring. Graph coloring is useful for problems like scheduling and radio channel assignment. However, finding the minimum number of colors to color a graph is an NP-complete problem, meaning there is no known efficient algorithm. Some common graph coloring algorithms discussed are greedy algorithm and Welsh-Powell algorithm.
Graph Theory
A graph consists of a set of vertices and edges connecting pairs of vertices. Graph coloring assigns colors to vertices such that no adjacent vertices share the same color. The chromatic polynomial counts the number of valid colorings of a graph using a given number of colors. It was introduced to study the four color theorem and fundamental results were established in the early 20th century. The chromatic polynomial can be used to find the chromatic number of a graph.
Graph coloring
Hello all, This is the presentation of Graph Colouring in Graph theory and application. Use this presentation as a reference if you have any doubt you can comment here.
Graph coloring Algorithm
The document discusses graph coloring and its applications. It defines graph coloring as assigning colors to vertices of a graph such that no two adjacent vertices have the same color. Applications of graph coloring include frequency assignment in mobile networks, mapping coloration, scheduling problems, Sudoku puzzles, and register allocation. The minimum number of colors needed for a graph is called its chromatic number.
CS6702 Unit III coloring ppt
Graph coloring involves assigning colors to the vertices of a graph such that no two adjacent vertices have the same color. This is called a proper coloring. The minimum number of colors needed for a proper coloring is called the chromatic number. Chromatic partitioning and the chromatic polynomial are other concepts related to graph coloring. Graph coloring has applications in Sudoku puzzles, traffic signal design, scheduling exams, and other areas where resources need to be allocated without conflicts.
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Let G be a graph having P3 packing. A P3 packing preclusion number of the graph G is a set of minimum number of edges, whose deletion leaves the resulting graph without a P3 packing. A hexagonal mesh pyramid of n levels denoted as HXPn consists of a set of vertices arranged in n levels of a hexagonal mesh. A vertex with address (k,(x,y,z)) placed at level k, of HXnnetwork is connected to all its adjacent vertices. This vertex is also connected to all the vertices of the hexagon with center (k+1,(x,y,z)). In this paper we find out the P3 packing preclusion of HXPnis trivial.
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This document outlines a learning activity where students will apply their knowledge of graphs, tables, and equations to linear situations. It involves a team challenge activity exploring linear relationships. For homework, students are assigned problem #6 on page 235 of their textbook to further their understanding.
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This document outlines a lesson plan to teach students how to solve systems of linear equations. The lesson will have students use an online Gizmo simulation called "Solving Systems" to explore how to graphically determine the solutions to systems of linear equations. They will then learn to solve systems of linear equations algebraically and complete homework problems from their textbook.
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This document provides a lesson plan for learning how to solve systems of linear equations. The lesson includes an introductory activity called "Chubby Bunny" followed by two exploratory sections on solving systems algebraically through substitution and elimination methods with practice problems from the textbook on page 199 problem 4.
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The document outlines a lesson plan for October 9th with the learning goal of solving linear inequalities. The plan includes a launch activity to introduce solving inequalities followed by an explore activity to further practice solving inequalities, and concludes with a summary worksheet problem.
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This document outlines a lesson plan to teach linear systems of equations through three parts: launching with an example of Gerardo's work, exploring how to save for a bike through a real-world scenario, and summarizing with practice problems from a textbook.
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Graph colouring
This document discusses graph coloring, which involves assigning colors to the vertices of a graph such that no two adjacent vertices have the same color. It provides examples of problems that can be modeled as graph coloring, such as scheduling committee meetings. The key points covered include defining graph coloring and chromatic number, discussing greedy algorithms and their limitations for graph coloring, and presenting the Welsh-Powell algorithm as an approach to graph coloring.
Graph coloring and_applications
Graph coloring involves assigning colors to objects in a graph subject to constraints. Vertex coloring assigns colors to vertices such that no adjacent vertices share the same color. The chromatic number is the minimum number of colors needed. Graph coloring has applications in scheduling, frequency assignment, and register allocation. Register allocation with chordal graphs can be done in polynomial time rather than NP-complete, since programs in SSA form have chordal interference graphs. A greedy algorithm can color chordal graphs in linear time, enabling simple and optimal register allocation.
Edge Coloring & K-tuple coloring
This document discusses edge coloring and k-tuple coloring in graph theory and computer applications. It defines edge coloring as assigning colors to edges so that edges incident to a common vertex have different colors. The minimum number of colors needed is the edge chromatic number. It also defines k-tuple coloring as assigning a set of k colors to each vertex such that no two adjacent vertices share a color, with Xk(G) being the minimum number of colors needed. An example shows C4 requires at least 4 colors for 2-tuple coloring.
Graph coloring problem
The document discusses graph coloring and its applications. It defines graph coloring as assigning colors to graph vertices such that no adjacent vertices have the same color. It also discusses the four color theorem, which states that any planar map can be colored with four or fewer colors. Finally, it provides an overview of backtracking as an algorithmic approach for solving graph coloring problems.
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This document discusses graph coloring and bipartite graphs. It defines a bipartite graph as one whose nodes can be partitioned into two sets such that no two nodes within the same set are adjacent. Bipartite graphs can be colored with two colors by coloring all nodes in one set one color and nodes in the other set the other color. The four color theorem states that any separation of a plane into contiguous regions can be colored with no more than four colors such that no two adjacent regions have the same color. Applications of graph coloring include exam scheduling, radio frequency assignment, register allocation, map coloring, and Sudoku puzzles.
Graph coloring using backtracking
This document summarizes graph coloring using backtracking. It defines graph coloring as minimizing the number of colors used to color a graph. The chromatic number is the fewest colors needed. Graph coloring is NP-complete. The document outlines a backtracking algorithm that tries assigning colors to vertices, checks if the assignment is valid (no adjacent vertices have the same color), and backtracks if not. It provides pseudocode for the algorithm and lists applications like scheduling, Sudoku, and map coloring.
GRAPH COLORING AND ITS APPLICATIONS
Graph Coloring and Its applications
Project for HERITAGE INSTITUTE OF TECHNOLOGY
1st semester CSE dept.
Graph Coloring : Greedy Algorithm & Welsh Powell Algorithm
This document summarizes a presentation on graph coloring. Graph coloring involves assigning colors to the vertices of a graph such that no two adjacent vertices have the same color. It has applications in problems like channel assignment. The document defines key terms like k-coloring, chromatic number, and k-chromatic graphs. It also discusses the NP-complete nature of the graph coloring problem and summarizes basic greedy and Welsh-Powell algorithms for graph coloring.
Graph coloring
This document presents information about graph coloring. It defines graph coloring as assigning colors to the vertices of a graph so that no adjacent vertices have the same color. There are two types: edge coloring and vertex coloring. Graph coloring is useful for problems like scheduling and radio channel assignment. However, finding the minimum number of colors to color a graph is an NP-complete problem, meaning there is no known efficient algorithm. Some common graph coloring algorithms discussed are greedy algorithm and Welsh-Powell algorithm.
Graph Theory
A graph consists of a set of vertices and edges connecting pairs of vertices. Graph coloring assigns colors to vertices such that no adjacent vertices share the same color. The chromatic polynomial counts the number of valid colorings of a graph using a given number of colors. It was introduced to study the four color theorem and fundamental results were established in the early 20th century. The chromatic polynomial can be used to find the chromatic number of a graph.
Graph coloring
Hello all, This is the presentation of Graph Colouring in Graph theory and application. Use this presentation as a reference if you have any doubt you can comment here.
Graph coloring Algorithm
The document discusses graph coloring and its applications. It defines graph coloring as assigning colors to vertices of a graph such that no two adjacent vertices have the same color. Applications of graph coloring include frequency assignment in mobile networks, mapping coloration, scheduling problems, Sudoku puzzles, and register allocation. The minimum number of colors needed for a graph is called its chromatic number.
CS6702 Unit III coloring ppt
Graph coloring involves assigning colors to the vertices of a graph such that no two adjacent vertices have the same color. This is called a proper coloring. The minimum number of colors needed for a proper coloring is called the chromatic number. Chromatic partitioning and the chromatic polynomial are other concepts related to graph coloring. Graph coloring has applications in Sudoku puzzles, traffic signal design, scheduling exams, and other areas where resources need to be allocated without conflicts.
P3 Packing Preclusion for Hexagonal Mesh Pyramid
Let G be a graph having P3 packing. A P3 packing preclusion number of the graph G is a set of minimum number of edges, whose deletion leaves the resulting graph without a P3 packing. A hexagonal mesh pyramid of n levels denoted as HXPn consists of a set of vertices arranged in n levels of a hexagonal mesh. A vertex with address (k,(x,y,z)) placed at level k, of HXnnetwork is connected to all its adjacent vertices. This vertex is also connected to all the vertices of the hexagon with center (k+1,(x,y,z)). In this paper we find out the P3 packing preclusion of HXPnis trivial.
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Graph Coloring : Greedy Algorithm & Welsh Powell Algorithm
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This document outlines a learning activity where students will apply their knowledge of graphs, tables, and equations to linear situations. It involves a team challenge activity exploring linear relationships. For homework, students are assigned problem #6 on page 235 of their textbook to further their understanding.
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This document outlines a lesson plan to teach students how to solve systems of linear equations. The lesson will have students use an online Gizmo simulation called "Solving Systems" to explore how to graphically determine the solutions to systems of linear equations. They will then learn to solve systems of linear equations algebraically and complete homework problems from their textbook.
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Aug 27th
- 1. ALGEBRAIC REASONING August 28th – Algebraic Learning outcome:To use deductive reasoning in proving algebraic properties
- 2. AUGUST 28TH WARMUP Simplify the following expressions: 5(2n+3)-7 6(n+5) – 9 2
- 3. CLASSWORK P 54 #3-4
- 4. CLASSWORK P 54 #4 C D
- 5. P54 #5