A {em Roman dominating function} on a graph $G$ is a function$f:V(G)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}A {em restrained Roman dominating}function} $f$ is a {color{blue} Roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} The wei...

A set S ⊆ V (G) is a disjunctive dominating of graph G if for every v ∈ (G)\S, neighbor vertex in or has at least two vertices each distance 2 from v. We say that restrained (G)\S there exists u \ such uv E(G) exist distinct u, w dG(u, v) = dG(w, v). The minimum cardinality γdr(G) the domination number G. In this paper, we characterize sets some binary operations as join, corona and lexico...

For any graph G, let V (G) and E(G) denote the vertex set and the edge set of G respectively. The Boolean function graph B(G, L(G),NINC) of G is a graph with vertex set V (G) ∪ E(G) and two vertices in B(G, L(G),NINC) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G or to a vertex and an edge not incident to it in G. For brevity, this graph is d...

For any graph G, let V (G) and E(G) denote the vertex set and the edge set of G respectively. The Boolean function graph B(G, L(G),NINC) of G is a graph with vertex set V (G) ∪ E(G) and two vertices in B(G, L(G),NINC) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G or to a vertex and an edge not incident to it in G. For brevity, this graph is d...

background: considering the negative consequences of using physical restraints, we conducted this study to identify patients who are more frequently restrained in a psychiatric emergency ward as an initial step to limit the use of restraint to the minimum possible. methods: this was a retrospective case control study conducted in iran psychiatric hospital in tehran, iran. we reviewed the files ...