Domination Parameters in Hypertrees and Sibling trees

Abstract

A locating-dominating set (LDS) of a graph $G$ is a dominating set $S$ of $G$ such that for every two vertices $u$ and $v$ in $V(G)\setminus S$, $N(u)\cap S\ne N(v)\cap S$. The locating-domination number ${\gamma }^L(G)$ is the minimum cardinality of a LDS of $G$. Further if $S$ is a total dominating set then $S$ is called a locating-total dominating set. In this paper we determine the domination, total domination, locating-domination and locating-total domination numbers for hypertrees and sibling trees.

12 pages, 11 figures