| 完全多部图的符号边控制数的界 |
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| 引用本文： | 赵衍才.完全多部图的符号边控制数的界[J].数学研究及应用,2023,43(2):161-165. |
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| 作者姓名： | 赵衍才 |
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| 作者单位： | 无锡城市职业技术学院, 江苏 无锡 214153; 无锡环境科学与工程研究中心, 江苏 无锡 214153 |
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| 基金项目： | 国家自然科学基金(Grant No.71774078). |
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| 摘 要： | $f: E(G)\rightarrow\{-1,1\}$称为图$G =(V,E)$的一个符号边控制函数 (简称SEDF),如果$fe]=f(Ne])=\sum_{e''\in Ne]}f(e'')\geq1$对于图$G$的每条边$e\in E$都成立. $w(f)=\sum_{e\in E}f(e)$称为函数$f$的权. $G$的符号边控制数$\gamma_{s}\,''(G)$是指$G$的所有符号边控制函数的最小权.本文对完全多部图的符号边控制数进行研究.对于完全$r$-部图, 当$r$为偶数并且各部的顶点数相同的情况下,我们得到了这一参数的若干下界和上界.
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| 关 键 词： | 符号边控制 符号边控制数 完全多部图 |
| 收稿时间： | 2022/4/30 0:00:00 |
| 修稿时间： | 2022/8/22 0:00:00 |
Bounds of the Signed Edge Domination Number of Complete Multipartite Graphs |
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| Yancai ZHAO.Bounds of the Signed Edge Domination Number of Complete Multipartite Graphs[J].Journal of Mathematical Research with Applications,2023,43(2):161-165. |
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| Authors: | Yancai ZHAO |
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| Institution: | 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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| Abstract: | A function $f: E(G)\rightarrow\{-1,1\}$ is called a signed edge dominating function (SEDF for short) of $G$ if $fe]=f(Ne])= \sum_{e''\in Ne]}f(e'')\geq1$, 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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| Keywords: | signed edge domination signed edge domination number complete multipartite graph |
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