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Bounds on the vertex-edge domination number of a tree

Abstract

A vertex-edge dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every edge of $G$ is incident with a vertex of $D$ or a vertex adjacent to a vertex of $D$. The vertex-edge domination number of a graph $G$, denoted by $\gamma_{ve}(T)$, is the minimum cardinality of a vertex-edge dominating set of $G$. We prove that for every tree $T$ of order $n \ge 3$ with $l$ leaves and $s$ support vertices we have $(n-l-s+3)/4 \le \gamma_{ve}(T) \le n/3$, and we characterize the trees attaining each of the bounds.

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Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
COMPTES RENDUS MATHEMATIQUE pages 363 - 366,
ISSN: 1631-073X
Language:
English
Publication year:
2014
Bibliographic description:
Krishnakumari B., Venkatakrishnan Y., Krzywkowski M.: Bounds on the vertex-edge domination number of a tree// COMPTES RENDUS MATHEMATIQUE. -, nr. 352 (2014), s.363-366
Verified by:
Gdańsk University of Technology

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