Realizability problem for commuting graphs

Michael Giudici, B. Kuzma

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    © 2016 Australian Mathematical Publishing Association Inc.
    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.
    Original languageEnglish
    Pages (from-to)335-355
    JournalJournal of the Australian Mathematical Society
    Volume101
    Issue number3
    Early online date13 May 2016
    DOIs
    Publication statusPublished - Dec 2016

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