   Chapter 10.3, Problem 18ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Draw all nonisomorphic graphs with four vertices and three edges.

To determine

Draw all nonisomorphic graphs with four vertices and three edges.

Explanation

Given information:

nonisomorphic graphs with four vertices and three edges.

Calculation:

Two graphs are G and G’ (with vertices V ( G ) and V(G) respectively and edges E ( G ) and E(G) respectively) are isomorphic if there exists one-to-one correspondence such that

[u,v] is an edge in G[g(u),g(v)] is an edge of G.

We are interested in all nonisomorphic simple graphs with 4 vertices and at most 3 edges. Since the graph is not simple, parallel edges and loops can occur in the graph.

No parallel edges and no loops: Three possible graphs: star, triangle and path of length 3.

Parallel edges and regular edges: Three possible graphs: three parallel edges, two parallel edges and regular edge with common vertex, two parallel edges and regular edge with no common vertex

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