Commuting graphs and their generalized complements

K. A. Bhat, G. Sudhakara

Research output: Contribution to journalArticle

Abstract

In this paper we consider a graph G, a partition P = {V1, V2,: :: , Vκ} of V (G) and the generalized complements GP κ and GP κ(i) with respect to the partition P. We derive conditions to be satisfied by P so that G commutes with its generalized complements. Apart from the general characterization, we also obtain conditions on P = {V1, V2,: :: , Vκ} so that G commutes with its generalized complements for certain classes of graphs namely complete graphs, cycles and generalized wheels. In the process we obtain a commuting decomposition of regular complete k-partite graph Kn1,n2,:::,nk in terms of a Hamiltonian cycle and its kcomplement. We also get a commuting decomposition of a complete k-partite graph Kn1,n2,:::,nk in terms of a generalized wheel and its κ- complement, where n1,n2,:::,nk satisfy some conditions.

Original languageEnglish
Pages (from-to)63-84
Number of pages22
JournalMalaysian Journal of Mathematical Sciences
Volume12
Issue number1
Publication statusPublished - 01-01-2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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