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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.
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참고문헌 (6)
참고문헌 신청
B. Zelinka / 2001 / Signed total domination number of a graph / Czechoslovak Math. J 51 (2) : 225 ~ 229
C. P. Wang / / The signed k-domination numbers in graphs / Ars Combin. (to appear)
D. B. West / 2000 / Introduction to Graph Theory / Prentice-Hall
M. A. Henning / 2004 / Signed total domination in graphs / Discrete Math 278 (1) : 109 ~ 125
M. A. Henning / 2006 / On the signed total domatic number of a graph / Ars Combin 79 : 277 ~ 288
C. P. Wang / / The signed k-domination numbers in graphs / Ars Combin. (to appear)
D. B. West / 2000 / Introduction to Graph Theory / Prentice-Hall
M. A. Henning / 2004 / Signed total domination in graphs / Discrete Math 278 (1) : 109 ~ 125
M. A. Henning / 2006 / On the signed total domatic number of a graph / Ars Combin 79 : 277 ~ 288
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