On Semitotal Domination in Graphs
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Published:2019-10-31
Issue:4
Volume:12
Page:1410-1425
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ISSN:1307-5543
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Container-title:European Journal of Pure and Applied Mathematics
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language:
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Short-container-title:Eur. J. Pure Appl. Math.
Author:
Aniversario Imelda S.,Canoy Jr. Sergio R.,Jamil Ferdinand P.
Abstract
A set $S$ of vertices of a connected graph $G$ is a semitotal dominating set if every vertex in $V(G)\setminus S$ is adjacent to a vertex in $S$, and every vertex in $S$ is of distance at most $2$ from another vertex in $S$. A semitotal dominating set $S$ in $G$ is a secure semitotal dominating set if for every $v\in V(G)\setminus S$, there is a vertex $x\in S$ such that $x$ is adjacent to $v$ and that $\left(S\setminus\{x\}\right)\cup \{v\}$ is a semitotal dominating set in $G$. In this paper, we characterize the semitotal dominating sets and the secure semitotal dominating sets in the join, corona and lexicographic product of graphs and determine their corresponding semitotal domination and secure semitotal domination numbers.
Publisher
New York Business Global LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science
Cited by
4 articles.
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1. Outer-Connected Semitotal Domination in Graphs;European Journal of Pure and Applied Mathematics;2022-07-31
2. ISOLATE SEMITOTAL DOMINATION IN GRAPHS;Advances and Applications in Discrete Mathematics;2022-07-15
3. 2-OUTER-INDEPENDENT SEMITOTAL DOMINATION IN GRAPHS;Advances and Applications in Discrete Mathematics;2022-05-19
4. On Semitotal k-Fair and Independent k-Fair Domination in Graphs;European Journal of Pure and Applied Mathematics;2020-10-31