Discrete Maths - Graphs
31. If v is an isolated vertex in a graph (multigraph) G, then what is its degree?
- Option : A
- Explanation : 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
- Option : C
- Explanation : 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
- Option : B
- Explanation : 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.
