Homogeneously almost self-complementary graphs

Abstract We give necessary and sufficient conditions on n for there to exist a homogeneously almost self-complementary graph of order 2 n for the cases when n is an odd prime power, and when n is twice a prime. We introduce a unified approach to almost self-complementary graphs via brick assignments, and use it to construct several important families of homogeneously almost self-complementary graphs.

[1]  Hong Zhang.  Characterization of self-complementary symmetric digraphs , 1996, Discret. Math..

[2]  Joy Morris,et al.  Self-complementary circulant graphs , 1999, Ars Comb..

[3]  Cai Heng Li,et al.  On finite graphs that are self-complementary and vertex transitive , 1998, Australas. J Comb..

[4]  C. Praeger,et al.  On Partitioning the Orbitals of a Transitive Permutation Group , 2002 .

[5]  Primoz Potocnik,et al.  On almost self-complementary graphs , 2006, Discret. Math..

[6]  Hong Zhang,et al.  Self-complementary symmetric graphs , 1992, J. Graph Theory.

[7]  Mikhail Muzychuk.  On Sylow Subgraphs of Vertex-Transitive Self-Complementary Graphs , 1999 .

[8]  Wojciech Peisert.  All Self-Complementary Symmetric Graphs , 2001 .

[9]  H. Wielandt.  Zur Theorie der einfach transitiven Permutationsgruppen , 1936 .

[10]  Cheryl E. Praeger,et al.  Homogeneous factorisations of graphs and digraphs , 2006, Eur. J. Comb..

[11]  H. Wielandt,et al.  Zur Theorie der einfach transitiven Permutationsgruppen. II , 1950 .

[12]  Cheryl E. Praeger,et al.  Homogeneous factorisations of complete multipartite graphs , 2007, Discret. Math..

[13]  Primoz Potocnik,et al.  Self-complementary two-graphs and almost self-complementary double covers , 2007, Eur. J. Comb..

[14]  B. Huppert.  Endliche Gruppen I , 1967 .

[15]  D. E. Taylor.  Regular 2‐Graphs , 1977 .

[16]  Tian Khoon Lim.  Edge-Transitive Homogeneous Factorisations of Complete Graphs , 2006, math/0605253.

[17]  J. Müller,et al.  Group Theory , 2019, Computers, Rigidity, and Moduli.

[18]  S. B. Rao.  On regular and strongly-regular self-complementary graphs , 1985, Discret. Math..

[19]  Edward Dobson,et al.  Almost self-complementary circulant graphs , 2004, Discret. Math..