## THE EDGE-TO-VERTEX STEINER DOMINATION NUMBER OF A GRAPH

## THE EDGE-TO-VERTEX STEINER DOMINATION NUMBER OF A GRAPH

*J. John, S. Ancy Mary*

[**PDF**]

## Abstract

A set W E is said to be an edge-to-vertex Steiner dominating set of G if W is both an edge-to-vertex dominating set and a edge-to-vertex Steiner set of G. The edge-to-vertex Steiner domination number sev(G) of G is the minimum cardinality of its edge-to-vertex Steiner dominating set of G and any edge-to-vertex Steiner dominating set of cardinality sev(G) is a sev-set of G. Some general properties satis ed by this concept are studied. The edge-to-vertex Steiner domination number of certain classes of graphs are determined. Connected graph of size q 3 with edge-to-vertex Steiner domination number q or q1 are characterized. It is shown for every pair a; b of integers with 2 a b, there exists a connected graph G such that ev(G) = a and sev(G) = b.

## Keywords

Edge-to-vertex Steiner domination number, Edge-to-vertex Steiner number, Edge-to-vertex Steiner distance, Edge-to-vertex domination number.