Restrained Regular Domination on a Litact Graph - Shankarajyothi, G.; Reddy, G. Upender (Communications in Mathematics and Applications, 2025)
We present the first research on restrained regular domination, which is a variant of standard domination. Assume that  is a graph. If every vertex in  has at least one neighbour in both  and , and every vertex in  has an identical degree, then a set  is a ‘restrained regular dominating set’, abbreviated RRDS. The least cardinality of all G’s RRDS is the ‘RRD number of G’, represented by . We ascertain the optimal bounds that can be applied to , and we identify the most optimal lower bounds for  and , both  and  are connected. We also characterise those graphs satisfying these bounds.
Keywords: Graph; Litact graph; Regular domination number; Restrained domination number; Restrained regular domination number