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

Title & Authors
ON THE SIGNED TOTAL DOMINATION NUMBER OF GENERALIZED PETERSEN GRAPHS P(n, 2)
Li, Wen-Sheng; Xing, Hua-Ming; Sohn, Moo Young;

Abstract
Let G = (V,E) be a graph. A function $\small{f:V{\rightarrow}\{-1,+1\}}$ 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, $\small{{\gamma}^s_t(G)}$, 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 $\small{n{\geq}6}$, $\small{{\gamma}^s_t(P(n,2))=2[\frac{n}{3}}$$\small{]}$$\small{+2t}$, where $\small{t{\equiv}n(mod\;3)}$ and $\small{0 {\leq}t{\leq}2}$.
Keywords
signed total domination;generalized Petersen graph;
Language
English
Cited by
References
1.
J. Cao, W. Lin, and M. Shi, Total domination number of generalized Petersen graphs, Intelligent Information Management 1 (2009), 15-18.

2.
X. Fu, Y. Yang, and B. Jiang, On the domination number of generalized Petersen graphs P(n, 3), Ars Combin. 84 (2007), 373-383.

3.
X. Fu, Y. Yang, and B. Jiang, On the domination number of generalized Petersen graphs P(n, 2), Discrete Math. 309 (2009), no. 8, 2445-2451.

4.
T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1997.

5.
T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, 1998.

6.
M. A. Henning, Signed total domination in graphs, Discrete Math. 278 (2004), no. 1-3, 109-125.

7.
W. Li, H. Xing, and M. Y. Sohn, On the signed domination number of generalized Petersen graphs P(n, 2), Manuscript.

8.
E. Shan and T. C. E. Cheng, Remarks on the minus (signed) total domination in graphs, Discrete Math. 308 (2008), no. 15, 3373-3380.

9.
E. Shan and T. C. E. Cheng, Upper bounds on the upper signed total domination number of graphs, Discrete Appl. Math. 157 (2009), no. 5, 1098-1130.

10.
H. M. Xing, L. Sun, and X. G. Chen, Signed total domination in graphs, J. Beijing Inst. Technol. 12 (2003), no. 3, 319-321.

11.
B. Zelinka, Signed total domination numbers of a graph, Czechoslovak Mathematical Journal 51 (2001), no. 2, 225-229.