On the Existence of a Stable Complementing Permutation in a $t-sc$ Graph

Abstract

The class of $t-sc$ graphs constitutes a new generalization of self-complementary graphs. Many $t-sc$ graphs exhibit a stable complementing permutation. In this paper, we prove a sufficient condition for the existence of a stable complementing permutation in a $t-sc$ graph. We also construct several infinite classes of $t-sc$ graphs to show the stringency of our sufficient condition.