论平面图中 $$ k $$ 优势独立集的数量

IF 0.58 Q3 Engineering Journal of Applied and Industrial Mathematics Pub Date : 2024-04-26 DOI:10.1134/s1990478924010149

D. S. Taletskii

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引用次数: 0

摘要

摘要如果一个图顶点的集合（set$ J_k$ of graph vertices）的顶点是成对相邻的，并且每个不在（J_k \）中的顶点都至少与（J_k \）中的（k \）顶点相邻，那么这个图顶点的集合（set$ J_k \））就被称为（（k \）-主导独立集（（k \geq 1 \））。在本文中，我们得到了一些平面图类中(k\geq 2 $的(k\)支配独立集的数量的新上限。

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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On the Number of $$ k $$ -Dominating Independent Sets in Planar Graphs

Abstract

A set $ J_k $ of graph vertices is said to be $ k $-dominating independent ( $ k \geq 1 $) if its vertices are pairwise adjacent and every vertex not in $ J_k $ is adjacent to at least $ k $ vertices in $ J_k $. In the present paper, we obtain new upper bounds for the number of $ k $-dominating independent sets for $ k \geq 2 $ in some planar graph classes.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.