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REALIZABILITY PROBLEM FOR COMMUTING GRAPHS

Published online by Cambridge University Press:  13 May 2016

MICHAEL GIUDICI
Affiliation:
Centre for the Mathematics of Symmetry and Computation, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia email michael.giudici@uwa.edu.au
BOJAN KUZMA
Affiliation:
University of Primorska, Glagoljaška 8, SI-6000 Koper, Slovenia email bojan.kuzma@famnit.upr.si IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia
Corresponding

Abstract

We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph of some semigroup. Moreover, we obtain complete classifications of the graphs with an isolated vertex or edge that are the commuting graph of a group and the cycles that are the commuting graph of a centrefree semigroup.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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REALIZABILITY PROBLEM FOR COMMUTING GRAPHS
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