(a) Define degree of a vertex. Prove that the number of odd degree ve…

Previous year question for Discrete Mathematics.

Question

(a) Define degree of a vertex. Prove that the number of odd degree vertices in a graph is always even.

(b) Is it possible to construct a graph with 22 edges such that four of its vertices are of degree 5, two vertices of degree 7 and remaining vertices with degree 3? Justify your answer.

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