Vertex-transitive CIS graphs

E. Dobson, A. Hujdurović, M. Milanič, Gabriel Verret

    Research output: Contribution to journalArticle

    10 Citations (Scopus)

    Abstract

    © 2014 Elsevier Ltd. A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and only if it is well-covered, co-well-covered, and the product of its clique and stability numbers equals its order. A graph is irreducible if no two distinct vertices have the same neighborhood. We classify irreducible well-covered CIS graphs with clique number at most 3 and vertex-transitive CIS graphs of valency at most 7, which include an infinite family. We also exhibit an infinite family of vertex-transitive CIS graphs which are not Cayley.
    Original languageEnglish
    Pages (from-to)87-98
    JournalEuropean Journal of Combinatorics
    Volume44
    Issue numberA
    DOIs
    Publication statusPublished - Feb 2015

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