SIGNED TOTAL κ-DOMATIC NUMBERS OF GRAPHS

Title & Authors
SIGNED TOTAL κ-DOMATIC NUMBERS OF GRAPHS
Khodkar, Abdollah; Sheikholeslami, S.M.;

Abstract
Let $\small{{\kappa}}$ be a positive integer and let G be a simple graph with vertex set V(G). A function f : V (G) $\small{{\rightarrow}}$ {-1, 1} is called a signed total $\small{{\kappa}}$-dominating function if $\small{{\sum}_{u{\in}N({\upsilon})}f(u){\geq}{\kappa}}$ for each vertex $\small{{\upsilon}{\in}V(G)}$. A set $\small{{f_1,f_2,{\ldots},f_d}}$ of signed total $\small{{\kappa}}$-dominating functions of G with the property that $\small{{\sum}^d_{i=1}f_i({\upsilon}){\leq}1}$ for each $\small{{\upsilon}{\in}V(G)}$, is called a signed total $\small{{\kappa}}$-dominating family (of functions) of G. The maximum number of functions in a signed total $\small{{\kappa}}$-dominating family of G is the signed total k-domatic number of G, denoted by $\small{d^t_{kS}}$(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 signed total $\small{{\kappa}}$-domatic numbers of complete graphs and complete bipartite graphs.
Keywords
signed total $\small{{\kappa}}$-domatic number;signed total $\small{{\kappa}}$-dominating function;signed total $\small{{\kappa}}$-domination number;
Language
English
Cited by
1.
SIGNED TOTAL {K}-DOMINATION AND {K}-DOMATIC NUMBERS OF GRAPHS, Discrete Mathematics, Algorithms and Applications, 2012, 04, 01, 1250006
2.
Signed mixed dominating functions in complete bipartite graphs, International Journal of Computer Mathematics, 2015, 92, 4, 712
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