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First prove the statement for the base case

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Let G = (V, E) be a graph in which V = {a1, a2, · · · , an} is the set of its nodes and E ={(ai, aj )|1 ≤ i, j ≤ n}, is the set of its edges. Let di be the degree of each node ai. By induction, provethat the sum of all degrees in the graph is an even number, i.e. Pni=1 di = 2 · K where K ∈ N.a) Basis: First prove the statement for the base case - where you have a graph with only one edge.b) Induction step: Suppose that the statement is true for a graph with some m edges, and prove it willbe true if you added one more edge to the graph.

Reference no: EM13994633

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