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1.1.30. Let G be a simple graph with adjacency matrix A and incidence matrix M. Prove that the degree of vi is the ith diagonal entry in A2 and in MMT. What do the entries in position (i, j) of A2 and MMT say about G?

1.1.30. Let G be a simple graph with adjacency matrix A and incidence matrix M. Prove that the degree of vi is the ith diagonal entry in A2 and in MMT. What do the entries in position (i, j) of A2 and MMT say about G?

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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1.1.30. Let G be a simple graph with adjacency matrix A and incidence matrix M. Prove that the degree of vi is the ith diagonal entry in A2 and in MMT. What do the entries in position (i, j) of A2 and MMT say about G?
Transcribed Image Text:1.1.30. Let G be a simple graph with adjacency matrix A and incidence matrix M. Prove that the degree of vi is the ith diagonal entry in A2 and in MMT. What do the entries in position (i, j) of A2 and MMT say about G?
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