The Class of $t$-sc Graphs and Their Stable Complementing Permutations

Abstract

In this paper, we present a new generalization of the self-complementary graphs, called the $t$-sc graphs. Various properties of this class of graphs are studied, generalizing earlier results on self-complementary graphs. Certain existential results on $t$-sc graphs are presented, followed by the construction of some infinite classes of $t$-sc graphs. Finally, the notion of $t$-sc graphs is linked with the notion of factorization, leading to a generalization of $r$-partite self-complementary graphs.