A new construction of regular and quasi-regular self-complementary graphs

Document Type : Short notes

Authors

1 Department of Mathematics, M.E.S’s Abasaheb Garware College, Pune-411004, India

2 Department of Mathematics, College of Engineering Pune, Pune-411006, India

Abstract

A graph G with a vertex set V and an edge set E is called regular if the degree of every vertex is the same. A quasi-regular graph is a graph whose vertices have one of two degrees r and r−1, for some positive integer r. A graph G is said to be self-complementary if G is isomorphic to it's complement G―. In this paper we give a new method for construction of regular and quasi-regular self-complementary graph.

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References

[1] C.R.J Clapham and D.J. Kleitman, The degree sequences of self-complementary graphs, J. Comb. Theory. Ser. B 20 (1976), no. 1, 67–74.  https://doi.org/10.1016/0095-8956(76)90068-X
[2] A. Farrugia, Self-complementary graphs and generalisations: a comprehensive reference manual, Ph.D. thesis, University of Malta, 1999.
[3] R.A. Gibbs, Self-complementary graphs, J. Comb. Theory. Ser. B 16 (1974), no. 2, 106–123. https://doi.org/10.1016/0095-8956(74)90053-7
[4] G. Ringel, Selbstkomplement¨are graphen, Arch. Math. 14 (1963), no. 1, 354–358. https://doi.org/10.1007/BF01234967.

[5] H. Sachs, ¨Uber selbstkomplement¨are graphen, Publ. Math. Drecen 9 (1962), no. 3–4, 270–288.
Communications in Combinatorics and Optimization
Volume 10, Issue 3
September 2025
Pages 595-599

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