On trees with total domination number equal to edge-vertex domination number plus one

Proceedings Mathematical Sciences

Y B Venkatakrishnan²  B Krishnakumari³  Marcin Krzywkowski¹ 

[1] Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Gdansk, Poland$$;Department of Pure and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa$$;Department of Mathematics, SASTRA University, Tanjore 0, India$$

关键词: Total domination;    edge-vertex domination;    tree.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

An edge $e in E(G)$ dominates a vertex $v in V(G)$ if $e$ is incident with $v$ or $e$ is incident with a vertex adjacent to $v$. An edge-vertex dominating set of a graph $G$ is a set $D$ of edges of $G$ such that every vertex of $G$ is edge-vertex dominated by an edge of $D$. The edge-vertex domination number of a graph $G$ is the minimum cardinality of an edge-vertex dominating set of $G$. A subset $D subseteq V(G)$ is a total dominating set of $G$ if every vertex of $G$ has a neighbor in $D$. The total domination number of $G$ is the minimum cardinality of a total dominating set of $G$. We characterize all trees with total domination number equal to edge-vertex domination number plus one.

【 授权许可】

Unknown