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 |
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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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