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Bounds on the number of edges in a graph. (a) Let G be an undirected graph...

Bounds on the number of edges in a graph.

(a)

Let G be an undirected graph with n vertices. Let Δ(G) be the maximum degree of any vertex in G, δ(G) be the minimum degree of any vertex in G, and m be the number of edges in G. Prove that

δ(G)n2≤m≤Δ(G)n2

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Solution Given a graph G-(V.E) We have, degree of vertex is deg(v)-2E1 Assume|E-m , then Σ deg(v)-21ml = 2m From the given qu

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