The Class of \(t\)-sc Graphs and Their Stable Complementing Permutations

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.