On Steiner domination in graphs

Samir K Vaidya; Raksha N Mehta

doi:10.26637/MJM0602/0013

Abstract

The steiner dominating set is a variant of dominating set in graphs. For a non - empty set $W$ of vertices in a connected graph $G$, the steiner distance $d(W)$ of $W$ is the minimum size of a connected subgraph $G$ containing $W$. Necessarily, each such subgraph is a tree and is called a steiner tree or a steiner $W$ - tree. The set of all vertices of $G$ that lie on some steiner $W$ - tree is denoted by $S(W)$. If $S(W)=V(G)$ then $W$ is called a steiner set for $G$. The steiner number $s(G)$ is the minimum cardinality of a steiner set. The minimum cardinality of a steiner dominating set is called the steiner domination number of graph. We present here some new results on steiner domination in graphs.

Keywords:

Dominating set, domination number, steiner dominating set, steiner domination number

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Samir K Vaidya Department of Mathematics, Saurashtra University, Rajkot - 360 005, Gujarat, India.
Raksha N Mehta Atmiya Institute of Technology and Science, Rajkot - 360 005, Gujarat, India.

Pages: 381-384
Date Published: 01-04-2018
Vol. 6 No. 02 (2018): Malaya Journal of Matematik (MJM)

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