Variants of the domination number for flower snarks

IF 0.6 3区数学 Q3 MATHEMATICS

Ars Mathematica Contemporanea Pub Date : 2021-10-05 DOI:10.26493/1855-3974.2710.f3d

R. Burdett, M. Haythorpe, Alex Newcombe

引用次数: 2

Abstract

We consider the flower snarks, a widely studied infinite family of 3--regular graphs. For the Flower snark $J_n$ on $4n$ vertices, it is trivial to show that the domination number of $J_n$ is equal to $n$. However, results are more difficult to determine for variants of domination. The Roman domination, weakly convex domination, and convex domination numbers have been determined for flower snarks in previous works. We add to this literature by determining the independent domination, 2-domination, total domination, connected domination, upper domination, secure Domination and weak Roman domination numbers for flower snarks.

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花刺的支配数的变体

我们考虑花结点，一个被广泛研究的无限3正则图族。对于Flower snark $J_n$在$4n$顶点上，证明$J_n$的支配数等于$n$是很简单的。然而，对于支配的变体，结果更难确定。在以前的著作中，已经确定了花纹的罗马支配、弱凸支配和凸支配数。我们通过确定独立统治，2统治，总统治，连接统治，上层统治，安全统治和弱罗马统治数来增加这一文献。

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

Ars Mathematica Contemporanea MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.