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2012 Induced subgraphs of Johnson graphs
Ramin Naimi, Jeffrey Shaw
Involve 5(1): 25-37 (2012). DOI: 10.2140/involve.2012.5.25

Abstract

The Johnson graph J(n,N) is defined as the graph whose vertices are the n-subsets of the set {1,2,,N}, where two vertices are adjacent if they share exactly n1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before. We give some necessary conditions and some sufficient conditions for a graph to be JIS, including: in a JIS graph, any two maximal cliques share at most two vertices; all trees, cycles, and complete graphs are JIS; disjoint unions and Cartesian products of JIS graphs are JIS; every JIS graph of order n is an induced subgraph of J(m,2n) for some mn. This last result gives an algorithm for deciding if a graph is JIS. We also show that all JIS graphs are edge move distance graphs, but not vice versa.

Citation

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Ramin Naimi. Jeffrey Shaw. "Induced subgraphs of Johnson graphs." Involve 5 (1) 25 - 37, 2012. https://doi.org/10.2140/involve.2012.5.25

Information

Received: 4 August 2010; Revised: 1 July 2011; Accepted: 9 July 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1246.05048
MathSciNet: MR2924311
Digital Object Identifier: 10.2140/involve.2012.5.25

Subjects:
Primary: 05C62

Rights: Copyright © 2012 Mathematical Sciences Publishers

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