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.