On a conjecture of Eǧecioǧlu and Iršič

IF 1 3区数学 Q3 MATHEMATICS, APPLIED Discrete Applied Mathematics Pub Date : 2025-05-15 Epub Date: 2025-01-21 DOI:10.1016/j.dam.2025.01.020

Jianxin Wei , Yujun Yang

引用次数: 0

Abstract

In 2021, Ö. Eǧecioǧlu, V. Iršič introduced the concept of Fibonacci-run graph

R_{n}

as an induced subgraph of Hypercube. They conjectured that the diameter of

R_{n}

is given by

n - ⌊ {(1 + \frac{n}{2})}^{\frac{1}{2}} - \frac{3}{4} ⌋

. In this paper, we introduce the concept of distance-barriers between vertices in

R_{n}

and provide a lower bound for the diameter of

R_{n}

via this concept. By constructing different types of distance-barriers, we show that the conjecture fails to hold for all

n \geq 230

and for some

n

between 91 and 229. The lower bounds obtained turn out to be better than the result given in the conjecture.

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关于Eǧecioǧlu和Iršič的猜想

2021年，Ö。Eǧecioǧlu， V. Iršič介绍了斐波那契运行图Rn作为超立方的诱导子图的概念。他们推测，Rn的直径为n−⌊（1+n2）12−34⌋。在本文中，我们引入了Rn中顶点间距离障碍的概念，并通过这个概念给出了Rn直径的下界。通过构造不同类型的距离障碍，我们证明了对于所有n≥230以及在91和229之间的某个n，该猜想不成立。所得到的下界比猜想中给出的结果要好。

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.

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