ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2017-2018): c. 84%
Discussiones Mathematicae Graph Theory 32(3) (2012)
Department of Mathematics University of Mohaghegh Ardabili P. O. Box 5919911367, Ardabil, Iran
We know that for any graph G of order n with minimum degree at
least k, γ×k(G) ≤ γ×k,t(G) ≤ n. Obviously for every k
-regular graph, the upper bound n is sharp. Here, we give a
sufficient condition for γ×k,t(G) < n. Then we
multipartite graphs G with γ×k(G) = γ×k,t(G).
We also state that the total k-domination number of a graph is the k
-transversal number of its open neighborhood hypergraph, and also
the domination number of a graph is the transversal number of its
neighborhood hypergraph. Finally, we give an upper bound for the total k
-domination number of the cross product graph G×H of two
graphs G and H in terms on the similar numbers of G and H.
Also, we show that this upper bound is strict for some graphs, when
k = 1.
Keywords: total k-domination (k-tuple total domination) number, k-tuple domination number, k-transversal number
2010 Mathematics Subject Classification: 05C69.
Received 9 March 2011 Revised 23 July 2011 Accepted 25 July 2011