Total Domination Number of Generalized Petersen Graphs P(ck,k)

Wensheng Li; Fengjun Liu; Liqiang Fan; Wei Chen; Jie Fang

doi:10.9734/BJMCS/2016/27588

Research Article Open access CC BY 4.0

Total Domination Number of Generalized Petersen Graphs P(ck,k)

Wensheng Li, Fengjun Liu, Liqiang Fan, Wei Chen, Jie Fang

Journal of Advances in Mathematics and Computer Science · pp. 1–7 · Published 31 Jul 2016

10.9734/BJMCS/2016/27588

Abstract

A set S of vertices of a graph G = (V, E) with no isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number is the minimum cardinality of a total dominating set of G. In this paper, we study the total domination in generalized Petersen graphs P(ck,k). The upper bounds of the total domination number of generalized Petersen graphs P(3k,k) and P(4k,k) are obtained.

Total domination number generalized Petersen graph upper bound.

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Wensheng Li, Fengjun Liu, Liqiang Fan, Wei Chen, Jie Fang (2016). Total Domination Number of Generalized Petersen Graphs P(ck,k). Journal of Advances in Mathematics and Computer Science , 1–7. https://doi.org/10.9734/BJMCS/2016/27588

Affiliations

Wensheng Li — Department of Mathematics and Information Sciences, Langfang Teachers University, Langfang, 065000, China.
Fengjun Liu — Department of Mathematics and Information Sciences, Langfang Teachers University, Langfang, 065000, China.
Liqiang Fan — Department of Mathematics and Information Sciences, Langfang Teachers University, Langfang, 065000, China.
Wei Chen — Department of Mathematics and Information Sciences, Langfang Teachers University, Langfang, 065000, China.
Jie Fang — Department of Mathematics and Information Sciences, Langfang Teachers University, Langfang, 065000, China.

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