树中的唯一最小半对支配集

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-11-25 DOI:10.7151/dmgt.2349

T. Haynes, Michael A. Henning

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引用次数: 1

摘要

摘要设G是具有顶点集V的图。子集S⊆V是G的半配对支配集，如果V \8838 S中的每个顶点都与S中的一个顶点相邻，并且S可以划分为两个元素子集，使得每个子集中的顶点相距最多两个距离。半配对支配数是G的半配对支配集的最小基数。我们刻画了具有唯一最小半配对支配集合的树。我们还确定了这些树的半配对支配数的上界，并刻画了达到该上界的树的特征。

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Unique Minimum Semipaired Dominating Sets in Trees

Abstract Let G be a graph with vertex set V. A subset S ⊆ V is a semipaired dominating set of G if every vertex in V \ S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number is the minimum cardinality of a semipaired dominating set of G. We characterize the trees having a unique minimum semipaired dominating set. We also determine an upper bound on the semipaired domination number of these trees and characterize the trees attaining this bound.

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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.