Discrete Structures Graphs

Special Graph Structures

Special cases of undirected graph structures:Complete graphs Kn

Cycles Cn

Wheels Wn

Bipartite graphs

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• 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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f

e d

c

b

g

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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f

e d

c

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• See Ex. 1,2,3,4,5,6,7. p-612 • Q. 1,3,5,7,11,17,19, 23, 27. p-61804/15/23

Exercise: Find the adjacency matrix

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a

dc

b

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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 subgraphMudasser Naseer 20 04/15/23