Graphs with Unique Maximum Packing of Closed Neighborhoods

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-06-29 DOI:10.7151/dmgt.2304

D. Bozovic, Iztok Peterin

引用次数: 3

Abstract

Abstract A packing of a graph G is a subset P of the vertex set of G such that the closed neighborhoods of any two distinct vertices of P do not intersect. We study graphs with a unique packing of the maximum cardinality. We present several general properties for such graphs. These properties are used to characterize the trees with a unique maximum packing. Two characterizations are presented where one of them is inductive based on five operations.

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闭邻域具有唯一最大包装的图

图G的包装是G的顶点集的子集P，使得P的任意两个不同顶点的闭邻域不相交。我们研究具有最大基数的唯一包装的图。我们给出了这类图的几个一般性质。这些特性用于表征具有唯一最大填充的树。给出了两个特征，其中一个是基于五个运算的归纳特征。

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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来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.