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CHARACTER GRAPHS WITH NONBIPARTITE HAMILTONIAN COMPLEMENT

Part of: Graph theory Representation theory of groups

Published online by Cambridge University Press:  25 November 2019

MAHDI EBRAHIMI Open the ORCID record for MAHDI EBRAHIMI [Opens in a new window]
MAHDI EBRAHIMI*
Affiliation:
School of Mathematics,Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran email m.ebrahimi.math@ipm.ir
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Abstract

For a finite group $G$, let $\unicode[STIX]{x1D6E5}(G)$ denote the character graph built on the set of degrees of the irreducible complex characters of $G$. In this paper, we obtain a necessary and sufficient condition which guarantees that the complement of the character graph $\unicode[STIX]{x1D6E5}(G)$ of a finite group $G$ is a nonbipartite Hamiltonian graph.

Keywords

character graphcharacter degreeHamiltonian graph

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 05C45: Eulerian and Hamiltonian graphs 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 91 - 95
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

This research was supported in part by a grant from the School of Mathematics, Institute for Research in Fundamental Sciences (IPM).

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