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arXiv · 1008.0595

Induced Subgraphs of Johnson Graphs

Ramin Naimi·Jeffrey Shaw
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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 n - 1 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 m <= n. 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.

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Ramin Naimi, Jeffrey Shaw. 2012-05-22. Induced Subgraphs of Johnson Graphs. https://doi.org/10.2140/involve.2012.5.25

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