Total Domination Number of Generalized Petersen Graphs P(ck,k)
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.
*Author to whom correspondence should be addressed.
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.
Keywords: Total domination number, generalized Petersen graph, upper bound.