On the defensive alliances in graph
| Autor: | Hasan Kharazi, Alireza Mosleh Tehrani |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Transactions on Combinatorics, Vol 8, Iss 1, Pp 1-14 (2019) |
| Druh dokumentu: | article |
| ISSN: | 2251-8657 2251-8665 |
| DOI: | 10.22108/toc.2018.50156.1396 |
| Popis: | Let $ G = (V,E) $ be a graph. We say that $ S \subseteq V $ is a defensive alliance if for every $ u \in S $, the number of neighbors $ u $ has in $ S $ plus one (counting $ u $) is at least as large as the number of neighbors it has outside $ S $. Then, for every vertex $ u $ in a defensive alliance $ S $, any attack on a single vertex by the neighbors of $ u $ in $ V-S $ can be thwarted by the neighbors of $ u $ in $ S $ and $ u $ itself. In this paper, we study alliances that are containing a given vertex $ u $ and study their mathematical properties. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
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