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n(n – 1) (c) Prove by induction that the number of edges of K, is (d) Sunnoca

n(n – 1) (c) Prove by induction that the number of edges of K, is (d) Sunnoca

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Write down the chromatic number of each of the graphs below. Justify your answer by colouring the graph. (i) Cube. (ii) Krst (iii) Wn 01 120 1000 1 (b) A graph G has adjacency matrix A = 10011 20.100 0 1 10 0 (i) Is Ga simple graph? (i) Write down the degree sequence for G. (c) Prove by induction that the number of edges of K, is 01-1). 2 (d) Suppose that a graph G is regular of degree r, where r is odd. (i) Prove that G has an even number of vertices. (ii) Prove that the numof G is a multiple of r. (e) A simple graph has 20 vertices. Any two distinct vertices u and v are such that deg(u) + deg(v) 2 20. Prove by contradiction that the graph is connected. Scientific WorkPlace
Transcribed Image Text:(a) Write down the chromatic number of each of the graphs below. Justify your answer by colouring the graph. (i) Cube. (ii) Krst (iii) Wn 01 120 1000 1 (b) A graph G has adjacency matrix A = 10011 20.100 0 1 10 0 (i) Is Ga simple graph? (i) Write down the degree sequence for G. (c) Prove by induction that the number of edges of K, is 01-1). 2 (d) Suppose that a graph G is regular of degree r, where r is odd. (i) Prove that G has an even number of vertices. (ii) Prove that the numof G is a multiple of r. (e) A simple graph has 20 vertices. Any two distinct vertices u and v are such that deg(u) + deg(v) 2 20. Prove by contradiction that the graph is connected. Scientific WorkPlace
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