Graphs

1. Discrete Structures
Graphs

2. Special Graph Structures
Special cases of undirected graph structures:
Complete graphs Kn
Cycles Cn
Wheels Wn
Bipartite graphs

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7. • See Ex. 5, 6, 7, 9, 10, 12. p-601
• Exercise Q. 4, 5, 7, 9, 21-25, 29 p-608

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a
f
e d
c
b
g

9. How to determine that a Graph is
Bipartite or not
• A graph is bipartite iff all its cycles are of even
length.
• For every edge, you can connect 2 vertices,
and those vertices can be different colors.
As long as every edge connects 2 vertices of
different color, you have a bipartite.
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a
f
e d
c
b

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16. • See Ex. 1,2,3,4,5,6,7. p-612
• Q. 1,3,5,7,11,17,19, 23, 27. p-618
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17. Exercise: Find the adjacency matrix
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dc
b

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20. Subgraphs
• A subgraph S of a graph G
is a graph such that
– The edges of S are a
subset of the edges of G
• A spanning subgraph of G
is a subgraph that contains
all the vertices of G
Subgraph
Spanning subgraph
Mudasser Naseer 20 01/12/15