On Steiner domination in graphs

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Authors :

Samir K Vaidya 1 * and Raksha N Mehta 2

Author Address :

1Department 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 – 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.



Article Info :

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



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