Let n E N with n > 2 and let G„ = (V, E) be the graph with vertex set V = {v1, v2, . . . , v2n} and edge set E = {{v¿, Vi+1} : 1 2. (b) Find all the cycles in Gn. (c) Out of the cycles you found in Gn, determine which are induced subgraphs.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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3. Let n eN with n > 2 and let G, = (V, E) be the graph with vertex set V = {v1, v2, ….., v2n}
and edge set
%3|
E = {{vi, vi+1} :1<i< 2n – 1} U{{v1, v2n}}U{{v1, Un+1}}.
These graphs are called “chord graphs", G2 and G3 are drawn below.
vi
v2
V6
G3
G2
U5
VA
v3
V4
(a) Find the value of |E(Gn)| for all n > 2.
(b) Find all the cycles in Gn.
(c) Out of the cycles you found in Gn, determine which are induced subgraphs.
1
Transcribed Image Text:3. Let n eN with n > 2 and let G, = (V, E) be the graph with vertex set V = {v1, v2, ….., v2n} and edge set %3| E = {{vi, vi+1} :1<i< 2n – 1} U{{v1, v2n}}U{{v1, Un+1}}. These graphs are called “chord graphs", G2 and G3 are drawn below. vi v2 V6 G3 G2 U5 VA v3 V4 (a) Find the value of |E(Gn)| for all n > 2. (b) Find all the cycles in Gn. (c) Out of the cycles you found in Gn, determine which are induced subgraphs. 1
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