Uniquely pairable graphs

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The concept of a k-pairable graph was introduced by Z. Chen [On k-pairable graphs, Discrete Mathematics 287 (2004), 11-15] as an extension of hypercubes and graphs with an antipodal isomorphism. In the present paper we generalize further this concept of a k-pairable graph to the concept of a semi-pairable graph. We prove that a graph is semi-pairable if and only if its prime factor decomposition contains a semi-pairable prime factor or some repeated prime factors. We also introduce a special class of k-pairable graphs which are called uniquely k-pairable graphs. We show that a graph is uniquely pairable if and only if its prime factor decomposition has at least one pairable prime factor, each prime factor is either uniquely pairable or not semi-pairable, and all prime factors which are not semi-pairable are pairwise non-isomorphic. As a corollary we give a characterization of uniquely pairable Cartesian product graphs.

Original languageEnglish (US)
Pages (from-to)6104-6110
Number of pages7
JournalDiscrete Mathematics
Volume308
Issue number24
DOIs
StatePublished - Dec 28 2008

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Prime factor
Decomposition
Graph in graph theory
If and only if
Product Graph
Decompose
Cartesian product
Discrete mathematics
Hypercube
Pairwise
Isomorphism
Corollary
Generalise
Concepts

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Che, Zhongyuan. / Uniquely pairable graphs. In: Discrete Mathematics. 2008 ; Vol. 308, No. 24. pp. 6104-6110.
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Uniquely pairable graphs. / Che, Zhongyuan.

In: Discrete Mathematics, Vol. 308, No. 24, 28.12.2008, p. 6104-6110.

Research output: Contribution to journalArticle

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