Vertices in all minimum paired-dominating sets of block graphs

Mathematics – Combinatorics

Scientific paper

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Scientific paper

Let $G=(V,E)$ be a simple graph without isolated vertices. A set $S\subseteq
V$ is a paired-dominating set if every vertex in $V-S$ has at least one
neighbor in $S$ and the subgraph induced by $S$ contains a perfect matching. In
this paper, we present a linear-time algorithm to determine whether a given
vertex in a block graph is contained in all its minimum paired-dominating sets.

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