Signed star domatic number of a graph |
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Authors: | M Atapour AN Ghameshlou |
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Institution: | a Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, Islamic Republic of Iran b Department of Mathematics, University of Mazandaran, Babolsar, Islamic Republic of Iran c Lehrstuhl II für Mathematik, RWTH-Aachen University, 52056 Aachen, Germany |
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Abstract: | Let G be a simple graph without isolated vertices with vertex set V(G) and edge set E(G). A function f:E(G)?{−1,1} is said to be a signed star dominating function on G if ∑e∈E(v)f(e)≥1 for every vertex v of G, where E(v)={uv∈E(G)∣u∈N(v)}. A set {f1,f2,…,fd} of signed star dominating functions on G with the property that for each e∈E(G), is called a signed star dominating family (of functions) on G. The maximum number of functions in a signed star dominating family on G is the signed star domatic number of G, denoted by dSS(G).In this paper we study the properties of the signed star domatic number dSS(G). In particular, we determine the signed domatic number of some classes of graphs. |
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Keywords: | Signed star domatic number Signed star dominating function Signed star domination number Regular graphs |
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