Combinatorics

Discrete mathematics

Graph

Mathematics

Data mining

Epistemology

Philosophy

Dominating set

Inverse

Geometry

Computer science

Simple (philosophy)

Vertex (graph theory)

Domination analysis

Cardinality (data modeling)

Discrete Mathematics Algorithms and Applications

Let [Formula: see text] be a connected simple graph. A dominating subset [Formula: see text] of [Formula: see text] is a fair dominating set of [Formula: see text] if all the vertices not in [Formula: see text] are dominated by the same number of vertices from [Formula: see text]. Let [Formula: see text] be a minimum fair dominating set of [Formula: see text]. A fair dominating set [Formula: see text] is called an inverse fair dominating set of [Formula: see text] with respect to [Formula: see text]. The inverse fair domination number of [Formula: see text] denoted by [Formula: see text] is the minimum cardinality of an inverse fair dominating set of [Formula: see text]. In this paper, we investigate the concept and give some important results. Further, we give the characterization of an inverse fair dominating set in the join and corona of two graphs.

Inverse fair domination in the join and corona of graphs