Bounds of the Signed Edge Domination Number of Complete Multipartite Graphs
Received:April 30, 2022  Revised:August 22, 2022
Key Words: signed edge domination   signed edge domination number   complete multipartite graph  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.71774078).
Author NameAffiliation
Yancai ZHAO Wuxi City College of Vocational Technology, Jiangsu 214153, P. R. China
Wuxi Environmental Science and Engineering Research Center, Jiangsu 214153, P. R. China 
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      A function $f: E(G)\rightarrow\{-1,1\}$ is called a signed edge dominating function (SEDF for short) of $G$ if $f[e]=f(N[e])= \sum_{e'\in N[e]}f(e')\geq1$, for every edge $e\in E(G)$. $w(f)=\sum_{e\in E}f(e)$ is called the weight of $f$. The signed edge domination number $\gamma_{s}\,'(G)$ of $G$ is the minimum weight among all signed edge dominating functions of $G$. In this paper, we initiate the study of this parameter for $G$ a complete multipartite graph. We provide the lower and upper bounds of $\gamma_{s}\,'(G)$ for $G$ a complete $r$-partite graph with $r$ even and all parts equal.
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