Graphs whose complement and square are isomorphic

M. Milanič, A.S. Pedersen, D. Pellicer, Gabriel Verret

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-complementary graphs, and characterize square-complementary graphs within various graph classes. The bipartite case turns out to be of particular interest. We also exhibit a square-complementary graph with a triangle, thus answering in the affirmative a question asked independently by Baltić et al. and by Capobianco and Kim. © 2014 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)62-75
    JournalDiscrete Mathematics
    Issue number1
    Publication statusPublished - 2014


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