﻿ Hossein Abdollahzadeh Ahangar

# Hossein Abdollahzadeh Ahangar

Babol Noshirvani University of Technology

## [ 1 ] - Total \$k\$-Rainbow domination numbers in graphs

Let \$kgeq 1\$ be an integer, and let \$G\$ be a graph. A {it\$k\$-rainbow dominating function} (or a {it \$k\$-RDF}) of \$G\$ is afunction \$f\$ from the vertex set \$V(G)\$ to the family of all subsetsof \${1,2,ldots ,k}\$ such that for every \$vin V(G)\$ with\$f(v)=emptyset \$, the condition \$bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}\$ is fulfilled, where \$N_{G}(v)\$ isthe open neighborhood of \$v\$. The {it weight} o...

## [ 2 ] - Bounds on the restrained Roman domination number of a graph

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...

## [ 3 ] - Some Results on the Maximal 2-Rainbow Domination Number in Graphs

A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...

نویسندگان همکار