a 2-emph{rainbow dominating function} (2rdf) on a graph $g=(v, e)$ is afunction $f$ from the vertex set $v$ to the set of all subsets of the set${1,2}$ such that for any vertex $vin v$ with $f(v)=emptyset$ thecondition $bigcup_{uin n(v)}f(u)={1,2}$ is fulfilled. a 2rdf $f$ isindependent (i2rdf) if no two vertices assigned nonempty sets are adjacent.the emph{weight} of a 2rdf $f$ is the value $o...

A subset D of V is called a dom strong dominating set if for every v V – D, there exists u1, u2 D such that u1v, u2v  E(G) and deg (u1 ) ≥ deg (v). The minimum cardinality of a dom strong dominating set is called dom strong domination number and is denoted by γdsd. In this paper, we introduce the concept of nonsplit dom strong domination number of a graph. A dom strong dominating set D of a ...

A vertex w in a connected graph G strongly resolves two distinct vertices u and v V (G) if is any shortest u-w path or v-w path. set W of strong resolving every are resolved by some W. S subset hop dominating for ∈ \ there exists such that dG(u, v) = 2. The smallest cardinality called the domination number G. This paper presents characterization sets join, corona lexicographic product graphs. F...

We solve several conjectures and open problems from a recent paper by Acharya [2]. Some of our results are relatives of the Nordhaus–Gaddum theorem, concerning the sum of domination parameters in hypergraphs and their complements. (A dominating set in H is a vertex set D ⊆ X such that, for every vertex x ∈ X\D there exists an edge E ∈ E with x ∈ E and E∩D 6= ∅.) As an example, it is shown that ...

In the initial stage we proposed the concept of Total Strong (Weak) domination in Fuzzy graph. It deal with the real time application that helps a individual person in crossing a road traffic signal. We will be giving a single value for vertices and edges. Enhancing the same concept, the Total Strong (Weak) domination in Intuitionistic Fuzzy graph was proposed. Here we will be giving a double v...