Let G=(V.E)be an undirected graph.Show thata)

Chapter , Problem 10E

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Problem 10E

Let G=(V.E)be an undirected graph.Show that

a) |N(v)|≤deg(v)for all v∈V.

b) |N(v)| = deg v for all v ∈ V if and only if G is a simple graph.

Suppose that S1, S2, .... Sn is a collection of subsets of a set S where n is a positive integer. A system of distinct representatives (SDR) for this family is an ordered  n-tuple (a1,a2,... ,an) with the property that  ai∈ Si for i = 1,2,....n  and ai≠ aj­ for all i ≠ j.