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

摘要

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.