Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 7, No 1 (2019): Electronic Journal of Graph Theory and Applications

Outer independent global dominating set of trees and unicyclic graphs

Doost Ali Mojdeh (Department of Mathematics, University of Mazandaran, Babolsar, Iran)
Mortaza Alishahi (Department of Mathematics, Islamic Azad University, Nazarabad Branch, Nazarabad, Iran, and Department of Mathematics, University of Tafresh, Tafresh, Iran.)



Article Info

Publish Date
05 Apr 2019

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 $\overline G$. γg(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 γgoi(G), is called the outer independent global domination number of G. An outer independent global dominating set of cardinality γgoi(G) is called a γgoi-set of G. In this paper we characterize trees T for which γgoi(T) = γ(T) and trees T for which γgoi(T) = γg(T) and trees T for which γgoi(T) = γoi(T) and the unicyclic graphs G for which γgoi(G) = γ(G), and the unicyclic graphs G for which γgoi(G) = γg(G).

Copyrights © 2019






Journal Info

Abbrev

ejgta

Publisher

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...