On the domination of triangulated discs

Noor A'lawiah Abd Aziz; Nader Jafari Rad; Hailiza Kamarulhaili

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 4, page 555-560
  • ISSN: 0862-7959

Abstract

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Let G be a 3 -connected triangulated disc of order n with the boundary cycle C of the outer face of G . Tokunaga (2013) conjectured that G has a dominating set of cardinality at most 1 4 ( n + 2 ) . This conjecture is proved in Tokunaga (2020) for G - C being a tree. In this paper we prove the above conjecture for G - C being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs.

How to cite

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Abd Aziz, Noor A'lawiah, Jafari Rad, Nader, and Kamarulhaili, Hailiza. "On the domination of triangulated discs." Mathematica Bohemica 148.4 (2023): 555-560. <http://eudml.org/doc/299557>.

@article{AbdAziz2023,
abstract = {Let $G$ be a $3$-connected triangulated disc of order $n$ with the boundary cycle $C$ of the outer face of $G$. Tokunaga (2013) conjectured that $G$ has a dominating set of cardinality at most $\frac\{1\}\{4\}(n+2)$. This conjecture is proved in Tokunaga (2020) for $G-C$ being a tree. In this paper we prove the above conjecture for $G-C$ being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs.},
author = {Abd Aziz, Noor A'lawiah, Jafari Rad, Nader, Kamarulhaili, Hailiza},
journal = {Mathematica Bohemica},
keywords = {domination; double domination; total domination; double total domination; planar graph; triangulated disc},
language = {eng},
number = {4},
pages = {555-560},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the domination of triangulated discs},
url = {http://eudml.org/doc/299557},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Abd Aziz, Noor A'lawiah
AU - Jafari Rad, Nader
AU - Kamarulhaili, Hailiza
TI - On the domination of triangulated discs
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 4
SP - 555
EP - 560
AB - Let $G$ be a $3$-connected triangulated disc of order $n$ with the boundary cycle $C$ of the outer face of $G$. Tokunaga (2013) conjectured that $G$ has a dominating set of cardinality at most $\frac{1}{4}(n+2)$. This conjecture is proved in Tokunaga (2020) for $G-C$ being a tree. In this paper we prove the above conjecture for $G-C$ being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs.
LA - eng
KW - domination; double domination; total domination; double total domination; planar graph; triangulated disc
UR - http://eudml.org/doc/299557
ER -

References

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