On Semitotal Domination in Graphs

Authors

  • Imelda S. Aniversario
  • Sergio R. Canoy Jr.
  • Ferdinand P. Jamil Department of Mathematics and Statistics, faculty, Mindanao State Unversity-Iligan Institute of Technology, Philippines

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i4.3501

Keywords:

semitotal dominating set, secure semitotal dominating set, semitotal domination number, secure semitotal domination number

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.

Author Biography

Ferdinand P. Jamil, Department of Mathematics and Statistics, faculty, Mindanao State Unversity-Iligan Institute of Technology, Philippines

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How to Cite

Aniversario, I. S., Canoy Jr., S. R., & Jamil, F. P. (2019). On Semitotal Domination in Graphs. European Journal of Pure and Applied Mathematics, 12(4), 1410–1425. https://doi.org/10.29020/nybg.ejpam.v12i4.3501

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