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Let's consider an undirected graph G = that for any vertices, i, j E I and there is no edge between i and j in E. A set i is a maximal independent set if no additional vertices of V can be added to I without violating its independence. Note, however, that a maximal independent set is not necessarily the largest independent set in G. Let a(G) denote the size of the largest maximal independent set in G. (V, E). An independent subset is a subset I c V such 1. What is a(G) if G is a complete graph on n vertices? What if G is a cycle on n vertices?

Let's consider an undirected graph G = that for any vertices, i, j E I and there is no edge between i and j in E. A set i is a maximal independent set if no additional vertices of V can be added to I without violating its independence. Note, however, that a maximal independent set is not necessarily the largest independent set in G. Let a(G) denote the size of the largest maximal independent set in G. (V, E). An independent subset is a subset I c V such 1. What is a(G) if G is a complete graph on n vertices? What if G is a cycle on n vertices?

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 80EQ
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Let's consider an undirected graph G = (V, E). An independent subset is a subset I C V such that for any vertices, i, j E I and there is no edge between i and j in E. A set i is a maximal independent set if no additional vertices of V can be added to I without violating its independence. Note, however, that a maximal independent set is not necessarily the largest independent set in G. Let a(G) denote the size of the largest maximal independent set in G. 1. What is a(G) if G is a complete graph on n vertices? What if G is a cycle on n vertices?
Transcribed Image Text:Let's consider an undirected graph G = (V, E). An independent subset is a subset I C V such that for any vertices, i, j E I and there is no edge between i and j in E. A set i is a maximal independent set if no additional vertices of V can be added to I without violating its independence. Note, however, that a maximal independent set is not necessarily the largest independent set in G. Let a(G) denote the size of the largest maximal independent set in G. 1. What is a(G) if G is a complete graph on n vertices? What if G is a cycle on n vertices?
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