完全图的对称覆盖和伪覆盖

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-07-15 DOI:10.1016/j.disc.2025.114677

Yan Zhou Zhu

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引用次数: 0

摘要

首先刻画了完全图的所有忠实弧传递盖，并给出了这些盖的一般构造。图Γ是其商Σ的伪覆盖，如果它们具有相同的价电子，并且Γ不是Σ的覆盖。作为本文的第二个结果，我们证明了当且仅当n−1不是素数时，完全图Kn具有连通弧传递伪覆盖。

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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Symmetric covers and pseudocovers of complete graphs

We first characterize all faithful arc-transitive covers of complete graphs and we give a general construction of such covers.

A graph Γ is a pseudocover of its quotient Σ if they have the same valency and Γ is not a cover of Σ. As the second result of this paper, we prove that the complete graph

K_{n}

has a connected arc-transitive pseudocover if and only if

n - 1

is not a prime.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.