On the signed total domination number of generalized Petersen graphs $P(n,2)$
Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 2021-2026
https://doi.org/10.4134/BKMS.2013.50.6.2021
Published online November 1, 2013
Wen-Sheng Li, Hua-Ming Xing, and Moo Young Sohn
Langfang Normal College, Tianjin University of Science $\&$ Technology, Changwon National University
Abstract : Let $G=(V,E)$ be a graph. A function $f:V\rightarrow\{-1,+1\}$ defined on the vertices of $G$ is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. The signed total domination number of $G$, $\gamma_t^s(G)$, is the minimum weight of a signed total dominating function of $G$. In this paper, we study the signed total domination number of generalized Petersen graphs $P(n,2)$ and prove that for any integer $n\geq 6$, $\gamma_t^s(P(n,2))= 2\lfloor \frac{n}{3} \rfloor + 2t$, where $t \equiv n (\mbox{mod }3)$ and $0\le t\le 2$.
Keywords : signed total domination, generalized Petersen graph
MSC numbers : 05C50, 05C69
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