| Elgin Kilic On Average Weighted Vertex Domination |
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| Abstract. Weighted graphs have an important role in network designs of many real life problems such as storing, security in systems, food supply planning, heavy traffic scheduling. Weighted domination has been studied widely on this scope. In this study a new view of average distance vertex domination is introduced. Every edge of the graph is labeled by positive numbers and each vertex is assigned by the average weight of all the edges adjacent to this vertex. Let D be a vertex dominating set of the graph, the weight of D is called the average vertex domination number where w(D) is minimum. |
| Keywords: Domination, weighted domination, average weight |
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| DOI: https://doi.org/10.54381/itta2024.27 |