（C3，C4，C5，C7）-自由几乎良控制图

Pub Date : 2022-07-12 DOI:10.7151/dmgt.2331

Hadi Alizadeh, Didem Gözüpek, Gülnaz Boruzanli Ekinci

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引用次数: 0

摘要

摘要图G的控制间隙被定义为G中最小控制集的最大基数和最小基数之间的差值。术语“好控制图”是指控制间隙为零的图，最早由Finbow等人提出。[好控制图：好覆盖图的集合，Ars Combin.25（1988）5–10]。本文主要研究具有控制间隙的图，称之为几乎完全控制图。虽然Finbow等人的结果对周长至少为8的几乎良支配图具有启示，但我们通过给出这些图的完整结构表征，将这些结果扩展到（C3，C4，C5，C7）-无几乎良支配的图。

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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(C3, C4, C5, C7)-Free Almost Well-Dominated Graphs

Abstract The domination gap of a graph G is defined as the di erence between the maximum and minimum cardinalities of a minimal dominating set in G. The term well-dominated graphs referring to the graphs with domination gap zero, was first introduced by Finbow et al. [Well-dominated graphs: A collection of well-covered ones, Ars Combin. 25 (1988) 5–10]. In this paper, we focus on the graphs with domination gap one which we term almost well-dominated graphs. While the results by Finbow et al. have implications for almost well-dominated graphs with girth at least 8, we extend these results to (C3, C4, C5, C7)-free almost well-dominated graphs by giving a complete structural characterization for such graphs.

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