Discrete Mathematics - Graph Theory
27. Degree of each vertex in kn is
- Option : B
- Explanation : Each vertex v is connected to the other n - 1 vertices; hence deg(v) = n - 1 for every v in kn.
There are five vertices, so
V = [P1,P2,P3,P4,P5] There are six edges and thus six pairs of vertices;
hence
E = [{P1, P4},{P2,P3}, {P2,P4}, {P2,P5}, {P4,P5}, {P3,P5}]
29. Degree of vertex P3 will be
- Option : 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
There are five vertices, so
V = [P1,P2,P3,P4,P5] There are six edges and thus six pairs of vertices;
hence
E = [{P1, P4},{P2,P3}, {P2,P4}, {P2,P5}, {P4,P5}, {P3,P5}]
30. Degree of vertex P5 will be
- Option : C
- 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
