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Discrete Mathematics MCQ - Graph Theory

31 If v is an isolated vertex in a graph (multigraph) G, then what is its degree?

The vertex v is isolated if it does not belong to any edge. Thus v is isolated if and only if deg(v) = O.
Consider the multigraph G where:
V(G) = [A,B,C,D] and
E(G) = [{A,C},{A,D},{B,B},{B,C},{C,A},{C,B},{D,B},{D,D}]

32 The degree of vertex D in G will be

Count the number of edges of which each vertex belongs or, equivalently count the number of times each vertex appears in E(G) to obtain deg(A) = 3, deg(B) = 5, deg(C) = 4, deg(D) = 4 Thus A and B are odd, and C and D are even.

33 The parity of vertex D will be

Count the number of edges of which each vertex belongs or, equivalently count the number of times each vertex appears in E(G) to obtain deg(A) = 3, deg(B) = 5, deg(C) = 4, deg(D) = 4 Thus A and B are odd, and C and D are even.

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Question:

Degree of vertex P3 will be

A. 1
B. 2
C. 3
D. none of these

Correct answer: B

Explanation:

Count the number of edges leaving each vertex to obtain deg(P1) = 1, deg(P2) = 3, deg(P3) = 2, deg(P4) = 3, deg(P5) = 3

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