On k-pairable graphs from trees

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Abstract

The concept of the k-pairable graphs was introduced by Zhibo Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11-15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter p(G), called the pair length of a graph G, as the maximum k such that G is k-pairable and p(G) = 0 if G is not k-pairable for any positive integer k. In this paper, we answer the two open questions raised by Chen in the case that the graphs involved are restricted to be trees. That is, we characterize the trees G with p(G) = 1 and prove that p(G □ H) = p(G) + p(H) when both G and H are trees.

Original languageEnglish (US)
Pages (from-to)377-386
Number of pages10
JournalCzechoslovak Mathematical Journal
Volume57
Issue number1
DOIs
StatePublished - Mar 1 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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