Question

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state an equation whicn states à relathn of AnB)and P(AB). 3. Prove each of the following two propositions on an undirected graph. 3.1. Every simple closed path contains a cycle. 3.2. Evevdeg(v) 2E. 4.1. What is the Euler circuit?

Answer 1

3.2) Since the degree of a vertex is the number of edges incident with that vertex, the sum of degree counts the total number of times an edge is incident with a vertex. Since every edge is incident with exactly two vertices,each edge gets counted twice,once at each end. Thus the sum of the degrees is equal twice the number of edges.

This theorem applies even if multiple edges and loops are present.

==> Σ deg_G(V) = 2E

oe comne have yele -