Commuting graphs and their generalized complements

Bhat, K A and Sudhakara, G (2018) Commuting graphs and their generalized complements. Malaysian Journal of Mathematical Sciences. pp. 63-84. ISSN 1823-8343

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Abstract

In this paper we consider a graph G, a partition P = fV1; V2; : : : ; Vkg of V (G) and the generalized complements GPk and GP k(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 = fV1; V2; : : : ; Vkg 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 k-complement, where n1; n2; : : : ; nk satisfy some conditions.

Item Type: Article
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 26 Jun 2018 06:26
Last Modified: 26 Jun 2018 06:26
URI: http://eprints.manipal.edu/id/eprint/151355

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