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On the characterization of trees with signed edge domination numbers 1, 2, 3, or 4 |
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| Authors: | Xiaoming Pi Huanping Liu |
| Institution: | a Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China b Department of Mathematics, Harbin Normal University, Harbin 150025, China c Department of Information Science, Harbin Normal University, Harbin 150025, China |
| Abstract: | Let G=(V,E) be a simple graph. For an edge e of G, the closed edge-neighbourhood of e is the set Ne]={e′∈E|e′ is adjacent to e}∪{e}. A function f:E→{1,−1} is called a signed edge domination function (SEDF) of G if ∑e′∈Ne]f(e′)≥1 for every edge e of G. The signed edge domination number of G is defined as  . In this paper, we characterize all trees T with signed edge domination numbers 1, 2, 3, or 4. |
| Keywords: | Graph Signed edge domination function Signed edge domination number |
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