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Question 1.9. Let Kn:r denote the Kneser graph, whose vertex set is the set of r-element subsets of an n-element sets, and where two vertices form an edge if the corresponding sets are disjoint. (a) Describe Kn:1 for n ≥ 1. (b) Draw K4:2 and K5:2. (c) Determine |E(Kn:r) for n ≥ 2r ≥ 1.

Question 1.9. Let Kn:r denote the Kneser graph, whose vertex set is the set of r-element subsets of an n-element sets, and where two vertices form an edge if the corresponding sets are disjoint. (a) Describe Kn:1 for n ≥ 1. (b) Draw K4:2 and K5:2. (c) Determine |E(Kn:r) for n ≥ 2r ≥ 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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the notation Kn:r for the Kneser graph, is different than the notation Kn,r for a complete bipartite graph.

 

Question 1.9. Let Kn:r denote the Kneser graph, whose vertex set is the set of r-element subsets of an n-element sets, and where two vertices form an edge if the corresponding sets are disjoint. (a) Describe Kn:1 for n ≥ 1. (b) Draw K4:2 and K5:2. (c) Determine |E(Kn:r) for n ≥ 2r ≥ 1.
Transcribed Image Text:Question 1.9. Let Kn:r denote the Kneser graph, whose vertex set is the set of r-element subsets of an n-element sets, and where two vertices form an edge if the corresponding sets are disjoint. (a) Describe Kn:1 for n ≥ 1. (b) Draw K4:2 and K5:2. (c) Determine |E(Kn:r) for n ≥ 2r ≥ 1.
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