Geodesic
On the domination of triangulated discs
Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 555-560

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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 $\frac 14(n+2)$. 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.
DOI : 10.21136/MB.2022.0122-21
Classification : 05C69
Keywords: domination; double domination; total domination; double total domination; planar graph; triangulated disc 
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Abd Aziz, Noor A'lawiah; Jafari Rad, Nader; Kamarulhaili, Hailiza. On the domination of triangulated discs. Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 555-560. doi: 10.21136/MB.2022.0122-21

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