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Let G be the simple graph on the vertex set V(G) = {a, b, c, d, e, f} with adjacency matrix: 011101 101110 1 1 0 0 0 0 1 1 0 0 1 0 010100 A = 100000 where row 1 corresponds to vertex a, row 2 to vertex b, etc. Without drawing the graph G, use the adjacency matrix A to: (a) find the degree of each vertex of G. (b) find the number of edges in G. (c) explain why G has no 6-cycle. (d) find the number of paths in G of length 2, starting at vertex b. (e) find the number of walks of length 3 from vertex 6 to vertex a in G.

Let G be the simple graph on the vertex set V(G) = {a, b, c, d, e, f} with adjacency matrix: 011101 101110 1 1 0 0 0 0 1 1 0 0 1 0 010100 A = 100000 where row 1 corresponds to vertex a, row 2 to vertex b, etc. Without drawing the graph G, use the adjacency matrix A to: (a) find the degree of each vertex of G. (b) find the number of edges in G. (c) explain why G has no 6-cycle. (d) find the number of paths in G of length 2, starting at vertex b. (e) find the number of walks of length 3 from vertex 6 to vertex a in G.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 72EQ
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Question 9 Let G be the simple graph on the vertex set V(G) = {a, b, c, d, e, f} with adjacency matrix: 011101 1 0 1 1 1 0 1 1 0 0 0 0 A = 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 where row 1 corresponds to vertex a, row 2 to vertex b, etc. Without drawing the graph G, use the adjacency matrix A to: (a) find the degree of each vertex of G. (b) find the number of edges in G. (c) explain why G has no 6-cycle. (d) find the number of paths in G of length 2, starting at vertex b. (e) find the number of walks of length 3 from vertex b to vertex a in G.
Transcribed Image Text:Question 9 Let G be the simple graph on the vertex set V(G) = {a, b, c, d, e, f} with adjacency matrix: 011101 1 0 1 1 1 0 1 1 0 0 0 0 A = 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 where row 1 corresponds to vertex a, row 2 to vertex b, etc. Without drawing the graph G, use the adjacency matrix A to: (a) find the degree of each vertex of G. (b) find the number of edges in G. (c) explain why G has no 6-cycle. (d) find the number of paths in G of length 2, starting at vertex b. (e) find the number of walks of length 3 from vertex b to vertex a in G.
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