On Steiner domination in graphs

On Steiner domination in graphs

**Authors : **

Samir K Vaidya^{ 1 *} and Raksha N Mehta ^{2}

**Author Address : **

^{1}Department of Mathematics, Saurashtra University, Rajkot - 360 005, Gujarat, India.

^{2 }Atmiya Institute of Technology and Science, Rajkot - 360 005, Gujarat, India.

*Corresponding author.

**Abstract : **

The steiner dominating set is a variant of dominating set in graphs. For a non â€“ 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 $W â€“$ tree. The set of all vertices of $G$ that lie on some steiner $W â€“$ 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.

**DOI : **

**Article Info : **

*Received : * November 12, 2017; *Accepted : * January 28, 2018.