February 9, 2023
Doost Ali Mojdeh

Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences

Research

Title Outer independent global dominating set of trees and unicyclic graphs
Type Article
Keywords
global domination, outer independent global dominating set, tree, unicyclic graph
Journal Electronic Journal of Graph Theory and Applications
DOI 10.5614/ejgta.2019.7.1.10
Researchers Doost Ali Mojdeh (First researcher) , Morteza Alishahi (Second researcher)

Abstract

Let G be a graph. A set D  V (G) is a global dominating set of G if D is a dominating set of G and G. g(G) denotes global domination number of G. A set D  V (G) is an outer independent global dominating set (OIGDS) of G if D is a global dominating set of G and V (G) 􀀀 D is an independent set of G. The cardinality of the smallest OIGDS of G, denoted by oi g (G), is called the outer independent global domination number of G. An outer independent global dominating set of cardinality oi g (G) is called a oi g -set of G. In this paper we characterize trees T for which oi g (T) = (T) and trees T for which oi g (T) = g(T) and trees T for which oi g (T) = oi(T) and the unicyclic graphs G for which oi g (G) = (G), and the unicyclic graphs G for which oi g (G) = g(G).