Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling$fcolon V(D)to {0, 1, 2}$such that every vertex with label $0$ has an in-neighbor with label $2$. A set ${f_1,f_2,ldots,f_d}$ ofRoman dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vin V(D)$,is called a {em Roman dominating family} (of functions) on $D$....

This study investigates the domination, double and regular domination in intuitionistic fuzzy hypergraph (IFHG), which has enormous application computer science, networking, chemical, biological engineering. Few properties of IFHG are established. Furthermore, definitions complement independent set given. The relation between an its was discussed. Moreover, illustrated by determining containmen...

In a graph G = (V (G), E(G)), a vertex dominates itself and its neighbors. A subset S of V (G) is a double dominating set if every vertex of V (G) is dominated at least twice by the vertices of S. The double domination number of G is the minimum cardinality among all double dominating sets of G. We consider the effects of edge removal on the double domination number of a graph. We give a necess...