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Let G = (V,E) be the graph with n vertices and m edges. (i) Define the incidence matrix B = (bij)1≤i≤n.1

Let G = (V,E) be the graph with n vertices and m edges. (i) Define the incidence matrix B = (bij)1≤i≤n.1

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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Let G = (V,E) be the graph with n vertices and m edges. (i) Define the incidence matrix B = (bij)1≤i≤n.1<j≤m of G. (ii) Define the oriented incidence matrix C = (Cij)1≤i≤n,1<j<m (iii) Recalling that the (i, j)-entry of the matrix CCT is given by Σ 1≤k≤m Ci,kCj.k explain what the entries of CCT correspond to in the graph G. (iv) Calculate the number of spanning trees of the graph with the following adjacency matrix: 0 1 0 1 1 10100 0101 0 10 10 1 100 10,
Transcribed Image Text:Let G = (V,E) be the graph with n vertices and m edges. (i) Define the incidence matrix B = (bij)1≤i≤n.1<j≤m of G. (ii) Define the oriented incidence matrix C = (Cij)1≤i≤n,1<j<m (iii) Recalling that the (i, j)-entry of the matrix CCT is given by Σ 1≤k≤m Ci,kCj.k explain what the entries of CCT correspond to in the graph G. (iv) Calculate the number of spanning trees of the graph with the following adjacency matrix: 0 1 0 1 1 10100 0101 0 10 10 1 100 10,
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