Connected edge Detour global domination number of a graph

A. Punitha Tharani; A. Ferdina

doi:10.26637/MJM0804/0042

Abstract

In this paper, we introduce the concept of connected edge detour global domination number of a graph is introduced. A subset $D$ of the vertex set $V(G)$ of a connected graph $G$ is called a connected edge detour global dominating set if $D$ is an edge detour global dominating set and the induced subgraph $\langle D\rangle$ is connected. The connected edge detour global domination number $\gamma_{c e d g}(G)$ of $G$ is the minimum cardinality taken over all connected edge detour global dominating sets in $\mathrm{G}$. A connected edge detour global dominating set of cardinality $\gamma_{c e d g}(G)$ is called a $\gamma_{c e d g}$-set of $G$. We determine $\gamma_{c e d g}(G)$ for some standard and special graphs and its properties are studied.

Keywords:

Edge detour global domination number, connected edge detour global domination number

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

A. Punitha Tharani Department of Mathematics, St. Mary’s College (Autonomous), Thoothukudi–628001, Tamil Nadu, India.
A. Ferdina Research Scholar [Register Number: 19122212092006], Department of Mathematics, St. Mary’s College (Autonomous), Thoothukudi–628001, Tamil Nadu, India.

Pages: 1580-1582
Date Published: 01-10-2020
Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

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