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Discrete Maths MCQ - Graphs

26 The number of colours required to properly colour the vertices of every planar graph is

27 Degree of each vertex in k_n is

Each vertex v is connected to the other n - 1 vertices; hence deg(v) = n - 1 for every v in k_n.

28 If G and G* are isomorphic graphs, then number of connected components of G* if G has connected components, are

The graphs G* must also have eight connected components.

GRPH-THEORY

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

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

GRPH-THEORY

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

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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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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