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

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Document Type : Original paper

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 $\overline{G}$. 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

Articles in Press, Accepted Manuscript
Available Online from 08 January 2024

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