This document provides an introduction and definitions for fundamental concepts in graph theory, including isomorphism, subgraphs, walks, and paths. Isomorphism refers to two graphs being identical in structure with a one-to-one correspondence between vertices and edges. A subgraph is a subset of vertices and edges from a larger graph where each edge in the subgraph connects the same endpoints. Walks are sequences of edges and vertices, while paths specifically refer to sequences where each consecutive edge shares an endpoint vertex and no vertex is repeated.

1. Fundamentals of
Graphs

2. Table of Contents:-
INTRODUCTION
ISOMORPHISM
SUB GRAPHS
WALKS
PATHS

3. Introduction
Agraph is determined as a mathematical structure that
represents a particular function by connecting a set of
points.

4. Isomorphism
IF WE ARE GIVEN TWO SIMPLE GRAPHS, G AND
H. GRAPHS G AND H ARE ISOMORPHIC IF THERE
IS A STRUCTURE THAT PRESERVES A ONE-TO-
ONE CORRESPONDENCE BETWEEN THE VERTICES
AND EDGES.

5. Sub Graphs
A GRAPH G1 = (V1, E1) IS CALLED A SUBGRAPH OF
A GRAPH G(V, E) IF V1(G) IS A SUBSET OF V(G)
AND E1(G) IS A SUBSET OF E(G) SUCH THAT EACH
EDGE OF G1 HAS SAME END VERTICES AS IN G.

6. A walk can be defined
as a sequence of
edgesandvertices of
a graph.
Walks

7. Paths
APATHIS ASEQUENCE OFEDGES THAT
BEGINS A
TAVERTEX, AND TRAVELS FROM
VERTEXTOVERTEXALONG EDGES OFTHE
GRAPH.

8. TH
AN
K YO
U
!