Question

The degree sequence of the simple graph G is 17, 7, 5, 4, 4, 2, 2,1 (a) How many edges does G have? (Briefly explain your answer.) (b) What is the degree sequence of G (Briefly explain your answer.)

Answer 1

Given Degree Sequence {7, 7, 5, 4, 4, 2, 2, 2, 1} a) How many edges does G have? According to Handshake Theorem any graph with vertices V_1, V_2, V_3, .., V_n and m edges has property as shown below 2m = Sigma^n_i = 1deg(v_i) = total degree Given sequence = 7, 7, 5, 4, 4, 2, 2, 2, 1 (These are degree's each vertex have) Total degree = 7 + 7 + 5 + 4 + 4 + 2 + 2 + 1 = 32 According to the above theorem m = Degree/2 = 32/2 = 16 Edges = 16 \r\n For suppose in a graph G if a vertex is joined to k number of vertices, then in the complemented graph vertices, then in the complemented graph it is joined to (Number of possible edges for each vertex) - K So, here possible edges are 7 for each vertex So, accordingly 7, 7, 5, 4, 4, 2, 2, 1