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

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Complement
Commute
Graph in graph theory
Wheel
Partition
Decompose
Hamiltonian circuit
Complete Graph
Cycle

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Commuting graphs and their generalized complements. / Bhat, K. A.; Sudhakara, G.

In: Malaysian Journal of Mathematical Sciences, Vol. 12, No. 1, 01.01.2018, p. 63-84.

Research output: Contribution to journalArticle

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