PreprintCC BY 4.0arXiv
On the (independent) semitotal domination in subdivision, middle, and central graphs
Abstract
A dominating set D of a nontrivial connected graph G is called a semitotal dominating set of G if every vertex in D is at distance at most two from another vertex in D. If, in addition, D is an independent set, then D is called an independent semitotal dominating set of G. The (independent) semitotal domination number of G is the minimum cardinality among all (independent) semitotal dominating sets of G. In this paper, we obtain closed formulas for these parameters in the following three well-known graph operators defined from a connected graph: the subdivision, middle, and central graphs.
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BibTeX
@misc{cabreramartinez2026independent,
title = {{On the (independent) semitotal domination in subdivision, middle, and central graphs}},
author = {Abel Cabrera-Martínez and José Luis López-Carmona and Ismael Rios-Villamar and Alejandro Serrano-Díaz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33932},
eprint = {2609.33932},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33932},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the (independent) semitotal domination in subdivision, middle, and central graphs
AU - Abel Cabrera-Martínez
AU - José Luis López-Carmona
AU - Ismael Rios-Villamar
AU - Alejandro Serrano-Díaz
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33932
UR - https://arxiv.org/abs/2609.33932
AB - A dominating set D of a nontrivial connected graph G is called a semitotal dominating set of G if every vertex in D is at distance at most two from another vertex in D. If, in addition, D is an independent set, then D is called an independent semitotal dominating set of G. The (independent) semitotal domination number of G is the minimum cardinality among all (independent) semitotal dominating sets of G. In this paper, we obtain closed formulas for these parameters in the following three well-known graph operators defined from a connected graph: the subdivision, middle, and central graphs.
ER -