Recall the degree sequence of an undirected graph is the sequence of the degrees
ID: 3684517 • Letter: R
Question
Recall the degree sequence of an undirected graph is the sequence of the degrees of the vertices of the graph in nonincreasing order, and that a sequence d_1, d_2, ..., d_n is called graphic. If it is the degree sequence of some simple graph? How many edges does a graph have if its degree sequence is 4, 3, 3, 2,2 Ans Is the sequence 4, 3, 3, 2, 1 a graphic sequence? Justify your answer. Ans. Consider the following four statements, some or all of which might possibly false? a. 12, 2, 1 is a graphic sequence b. 3, 2, 1? c. 18, 3, 2, 1 is a graphic sequence. d. 4, 3, 2, 1 Write down the degree of a Q_3 graph? Ans. Write down the degree of a rho_m graph? Write down the degree sequence of a u_2, u graph? Ans.Explanation / Answer
(a)
Number of edges = sum of degree sequence / 2
= (4 + 3 + 3 + 2 + 2) / 2
= (14) / 2
= 7
(b)
No, it is not a graphic sequence because sum of degree sequence should always be even.
(c)
- (a)
No, it is not a graphic sequence because sum of degree sequence should always be even.
- (b)
Yes it might be a degree sequence.
- (c)
Yes it might be a degree sequence.
- (d)
No, it is not a graphic sequence because sum of degree sequence should always be even.
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