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On the defensive alliances in graph | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 8، شماره 1، خرداد 2019، صفحه 1-14 اصل مقاله (262 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2018.50156.1396 | ||
| نویسندگان | ||
| Hasan Kharazi؛ Alireza Mosleh Tehrani* | ||
| Department of Mathematics, Faculty of Science, Iran University of Science and Technology, Tehran, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Defensive alliance؛ Alliances in graphs؛ Edge cut | ||
| مراجع | ||
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