Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE SIGNED TOTAL DOMINATION NUMBER OF GENERALIZED PETERSEN GRAPHS P(n, 2)

  • Li, Wen-Sheng (Department of Mathematics & Information Sciences Langfang Normal College) ;
  • Xing, Hua-Ming (School of Sciences Tianjin University of Science & Technology) ;
  • Sohn, Moo Young (Department of Mathematics Changwon National University)
  • Received : 2012.10.03
  • Published : 2013.11.30
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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, ${\gamma}^s_t(G)$, 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 $n{\geq}6$, ${\gamma}^s_t(P(n,2))=2[\frac{n}{3}]+2t$, where $t{\equiv}n(mod\;3)$ and $0 {\leq}t{\leq}2$.

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References

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