Restrained domination polynomial of join and corona of graphs
S. Velmurugan, R. Kala · Discrete Mathematics Algorithms and Applications · 2022
Let [Formula: see text] be a simple graph of order [Formula: see text]. A set [Formula: see text] is said to be a restrained set if each vertex in [Formula: see text] is adjacent to a vertex in [Formula: see text]. The restrained polynomial of a graph [Formula: see text] is [Formula: see text] where [Formula: see text] is the number of restrained sets of [Formula: see text] of cardinality [Formula: see text]. A set [Formula: see text] is said to be a restrained dominating set if each vertex in [Formula: see text] is adjacent to a vertex in [Formula: see text] and to a vertex in [Formula: see text]. The restrained domination polynomial of a graph [Formula: see text] is defined by [Formula: see text] where [Formula: see text] is the number of restrained dominating sets of [Formula: see text] of cardinality [Formula: see text]. In this paper, we derive restrained domination polynomial of join and corona of any two graphs.