The Signed Edge-Domatic Number of a Graph |
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Authors: | Xiang-Jun Li Jun-Ming Xu |
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Institution: | 1. Wentsun Wu Key Laboratory of CAS, School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, China 2. School of Information and Mathematics, Yangtze University, Jingzhou, 434023, Hubei, China
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Abstract: | For a nonempty graph G = (V, E), a signed edge-domination of G is a function ${f: E(G) \to \{1,-1\}}$ such that ${\sum_{e'\in N_{G}e]}{f(e')} \geq 1}$ for each ${e \in E(G)}$ . The signed edge-domatic number of G is the largest integer d for which there is a set {f 1,f 2, . . . , f d } of signed edge-dominations of G such that ${\sum_{i=1}^{d}{f_i(e)} \leq 1}$ for every ${e \in E(G)}$ . This paper gives an original study on this concept and determines exact values for some special classes of graphs, such as paths, cycles, stars, fans, grids, and complete graphs with even order. |
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