Inverse Outer Connected Domination Number of Jump Graph

Inverse Outer Connected Domination Number of Jump Graph

A. Sugirtha1
Research Scholar , Reg.No 22211282092008, PG and Research Department of Mathematics,

sugirtha1994@gmail.com

St. Xavier’s College (Autonomous), Palayamkottai, Tamil Nadu, India.

Y. Therese Sunitha Mary2
Assistant Professor and Head,

PG and Research Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai,

sunithanepolian@gmail.com

Tamil Nadu, India.

Affiliated to

Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli 627 012, Tamil Nadu.

Abstract

Let G be a graph with no isolated vertices. A collection of vertices D in G is the smallest outer connected dominating set. Consider Dr is the smallest inverse dominating set of G with respect to D. If the induced subgraph < V − Dr > is connected, then Dr is said to be an inverse outer connected dominating set. The inverse outer connected domination number γ˜r (G) is the smallest cardinality taken over all the minimal inverse outer connected dominating sets of G. The jump graph J(G) of the graph G is formed on E(G) such that two vertices are adjacent if and only if they are not adjacent in G. In this paper, We investigate the basic properties of inverse outer connected domination of jump graphs and their exact values for common graphs. The relationship between jump graph inverse outer connected domination and other characteristics is also examined.

Keywords     : Inverse domination, Jump graph, Outer connected domination, Inverse outer connected domination.

AMS subject classication (2020): 05C69 ,05C70,05C76.