SIGNED TOTAL k-DOMATIC NUMBERS OF GRAPHS

다국어 초록 (Multilingual Abstract)

Let k be a positive integer and let G be a simple graph with vertex set V(G). A function <수식> is called a signed total k-dominating function if <수식> for each vertex v ∈V(G). A set {f1, f2,..., fd} of signed total k-dominating functions of G with the property that <수식> for each v ∈ V(G), is called a signed total k-dominating family (of functions) of G. The maximum number of functions in a signed total k-dominating family of G is the signed total k-domatic number of G, denoted by d^t_(kS)(G). In this note we initiate the study of the signed total k-domatic numbers of graphs and present some sharp upper bounds for this parameter. We also determine the signed total k-domatic numbers of complete graphs and complete bipartite graphs.

참고문헌 (Reference)

1 C. P. Wang, "The signed k-domination numbers in graphs"

2 B. Zelinka, "Signed total domination number of a graph" 51 (51): 225-229, 2001

3 M. A. Henning, "Signed total domination in graphs" 278 (278): 109-125, 2004

4 M. Guan, "Signed total domatic number of a graph" 12 (12): 31-34, 2008

5 M. A. Henning, "On the signed total domatic number of a graph" 79 : 277-288, 2006

6 D. B. West, "Introduction to Graph Theory" Prentice-Hall 2000