On the signed total domination number of generalized Petersen graphs P(n,2)
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Let G = (V,E) be a graph. A function f : V → {−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, γs 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 ≥ 6, γs t (P(n, 2)) = [수식], where t ≡ n(mod 3) and 0 ≤ t ≤ 2.
Abstract
Let G = (V,E) be a graph. A function f : V → {−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, γs 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 ≥ 6, γs t (P(n, 2)) = [수식], where t ≡ n(mod 3) and 0 ≤ t ≤ 2.
참고문헌 (11)
- J. Cao, "Total domination number of generalized Petersen graphs", Intelligent Information Management, 1, pp.15~18 (2009)
- X. Fu, "On the domination number of generalized Petersen graphs P(n, 3)", Ars Combin, 84, pp.373~383 (2007)
- X. Fu, "On the domination number of generalized Petersen graphs P(n, 2)", Discrete Math, 309(8), pp.2445~2451 (2009)
- T. W. Haynes, "Domination in Graphs: Advanced Topics" (1997), Marcel Dekker
- T. W. Haynes, "Fundamentals of domination in graphs" (1998), Marcel Dekker
- M. A. Henning, "Signed total domination in graphs", Discrete Math, 278(1), pp.109~125 (2004)
- W. Li, "On the signed domination number of generalized Petersen graphs P(n, 2)", ~
- E. Shan, "Remarks on the minus (signed) total domination in graphs", Discrete Math, 308(15), pp.3373~3380 (2008)
- E. Shan, "Upper bounds on the upper signed total domination number of graphs", Discrete Appl. Math, 157(5), pp.1098~1130 (2009)
- H. M. Xing, "Signed total domination in graphs", J. Beijing Inst. Technol, 12(3), pp.319~321 (2003)
- B. Zelinka, "Signed total domination numbers of a graph", Czechoslovak Mathematical Journal, 51(2), pp.225~229 (2001)