The Roman domination number of some special classes of graphs - convex polytopes

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI:10.2298/AADM171211019K

Aleksandar Kartelj, Milana Grbić, Dragan Matic, V. Filipović

引用次数: 4

Abstract

In this paper we study the Roman domination number of some classes of planar graphs - convex polytopes: An, Rn and Tn. We establish the exact values of Roman domination number for: An, R3k, R3k+1, T8k, T8k+2, T8k+3, T8k+5 and T8k+6. For R3k+2, T8k+1, T8k+4 and T8k-1 we propose new upper and lower bounds, proving that the gap between the bounds is 1 for all cases except for the case of T8k+4, where the gap is 2.

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若干特殊图类的罗马统治数-凸多边形

本文研究了若干类平面凸多面体An、Rn和Tn的罗马支配数，给出了An、R3k、R3k+1、T8k、T8k+2、T8k+3、T8k+5和T8k+6的罗马支配数的精确值。对于R3k+2、T8k+1、T8k+4和T8k-1，我们提出了新的上界和下界，证明了除了T8k+4的上界和下界差为2外，其他情况下的上界和下界差均为1。

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

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).