Graphs with degree sequence {(m−1)m,(n−1)n} and {mn,nm}

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-08-26 DOI:10.1016/j.dam.2024.08.009

Boris Brimkov , Valentin Brimkov

引用次数: 0

Abstract

In this paper we study the class of graphs $G_{m, n}$ that have the same degree sequence as two disjoint cliques $K_{m}$ and $K_{n}$ , as well as the class ${\bar{G}}_{m, n}$ of the complements of such graphs. We establish various properties of $G_{m, n}$ and ${\bar{G}}_{m, n}$ related to recognition, connectivity, diameter, bipartiteness, Hamiltonicity, and pancyclicity. We also show that several classical optimization problems on these graphs are NP-hard, while others can be solved efficiently.

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阶数序列为 {(m-1)m,(n-1)n} 和 {mn,nm} 的图形

在本文中，我们研究了与两个不相交的小群 Km 和 Kn 具有相同度序列的一类图 Gm,n，以及这类图的补集 G¯m,n。我们建立了 Gm,n 和 G¯m,n 的与识别、连通性、直径、两部分性、汉密尔顿性和泛周期性有关的各种性质。我们还证明了这些图上的几个经典优化问题是 NP-困难的，而其他问题则可以高效求解。

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

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.