图的最小支配集的消去性质

Pub Date : 2022-11-25 DOI:10.7151/dmgt.2354

Jaume Martí-Farré, M. Mora, M. L. Puertas, José Luis Ruiz

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引用次数: 0

摘要

图的支配集是一个顶点子集，使得不在子集中的每个顶点都与该子集中的至少一个相邻。在本文中，我们研究了当存在一个新的支配集时，它包含（分别包含）通过从两个最小支配集的并集中移除公共顶点而获得的子集。提供了满足这种消去性质的图的完整描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Elimination Properties for Minimal Dominating Sets of Graphs

Abstract A dominating set of a graph is a vertex subset such that every vertex not in the subset is adjacent to at least one in the subset. In this paper we study whenever there exists a new dominating set contained (respectively, containing) the subset obtained by removing a common vertex from the union of two minimal dominating sets. A complete description of the graphs satisfying such elimination properties is provided.

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