Abstract
Let \(G\) be a graph with the vertex set \(V(G)\) and the edge set \(E(G)\). A function \(f: E(G)\longrightarrow \{-1, 1\}\) is said to be a signed star dominating function of \(G\) if \(\sum _{e \in E_G(v)}f (e)\ge 1 \), for every \(v \in V(G)\), where \(E_G(v) = \{uv\in E(G)\,|\,u \in V (G)\}\). The minimum values of \(\sum _{e \in E_G(v)}f (e)\), taken over all signed star dominating functions \(f\) on \(G\), is called the signed star domination number of \(G\) and denoted by \(\gamma _{SS}(G)\). In this paper we determine the signed star domination number of regular multigraphs.
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Zare, S., Rahmati, F. On the signed star domination number of regular multigraphs. Period Math Hung 68, 39–44 (2014). https://doi.org/10.1007/s10998-014-0026-3
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DOI: https://doi.org/10.1007/s10998-014-0026-3