Question

1. True or False? Support your answer. (a) There is a graph with degree sequence 1,1,1,1. (b) There is a graph with degree sequence 3, 3,3, 3. (c) There is a graph with degree sequence 3,2,1,1.

Answer 1

Firstly, we discuss some definition and properties for draw a graph from degree sequences. Degree sequence of a Graph A sequence d_1, d_2, - - - , d_n of non - negative integers is called degree sequence of a graph G if the vertices of G can be labeled v_1, v_2, - - -, v_n such that deg (v_i) = d_i for all I = 1, 2, - - -, n Firstly, we discuss some definition and properties for draw a graph from degree sequence. Degree sequence of a Graph Let d_1, d_2, - - -, d_n be the degree of the vertices v_1, v_2, - - -, v_n of a graph G such that d_1 lessthanorequalto d_2 lessthanorequalto - - - - -lessthanorequalto d_n, then the finite sequence (d_1, d_2,- - - -,d_n) is called the degree sequence of G. \r\n Properties for draw a graph from degree sequence. If the sum of the