增广立方体的两不相交环盖环性

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-04-20 DOI:10.1016/j.dam.2025.04.033

Dongqin Cheng

引用次数: 0

摘要

如果存在长度为 l(C)的两个顶点相交循环 C 和长度为 l(C′)的两个顶点相交循环 C′的集合，使得 l(C)+l(C′)=|V(G)|且 r1≤l(C)≤r2 ，则图 G 是双相交循环覆盖 [r1,r2]-pancyclic 的。增强立方体是超立方体的变体之一，具有许多超立方体所不具备的优良性质。在本文中，我们证明 n 维增强立方体 AQn 是两两相交循环覆盖 [3,2n-1]-pancyclic 的，其中 n≥3.

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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Two-disjoint-cycle-cover pancyclicity of augmented cubes

A graph

G

is two-disjoint-cycle-cover

[r_{1}, r_{2}]

-pancyclic if there is a collection of two vertex disjoint cycles

C

of length

l (C)

and

C^{'}

of length

l (C^{'})

such that

l (C) + l (C^{'}) = | V (G) |

and

r_{1} \leq l (C) \leq r_{2}

. The augmented cube is one of the variations of hypercube and possesses many good properties that the hypercube does not have. In this paper, we prove that the

n

-dimensional augmented cube

A Q_{n}

is two-disjoint-cycle-cover

[3, 2^{n - 1}]

-pancyclic, where

n \geq 3

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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.