SIGNED TOTAL k-DOMATIC NUMBERS OF GRAPHS
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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.
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 (6)
- M. Guan, "Signed total domatic number of a graph", J. Shanghai Univ, 12(1), pp.31~34 (2008)
- M. A. Henning, "Signed total domination in graphs", Discrete Math, 278(1), pp.109~125 (2004)
- M. A. Henning, "On the signed total domatic number of a graph", Ars Combin, 79, pp.277~288 (2006)
- C. P. Wang, "The signed k-domination numbers in graphs", Ars Combin. (to appear), ~
- D. B. West, "Introduction to Graph Theory" (2000), Prentice-Hall
- B. Zelinka, "Signed total domination number of a graph", Czechoslovak Math. J, 51(2), pp.225~229 (2001)