Bounds in radial Moore graphs of diameter 3

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-11 DOI:10.1016/j.disc.2025.114533

Jesús M. Ceresuela, Nacho López

引用次数: 0

Abstract

Radial Moore graphs preserve the order and the regularity of Moore graphs and allow some vertices to have more eccentricity than they should have in a Moore graph. One way to classify their resemblance with a Moore graph is the status measure. The status of a graph is defined as the sum of the distances of all pairs of ordered vertices and equals twice the Wiener index. Vertices with minimum eccentricity are called central vertices. In this paper we study upper bounds for both the maximum number of central vertices and the status of radial Moore graphs. Finally, we present a family of radial Moore graphs of diameter 3 that is conjectured to have maximum status.

查看原文本刊更多论文

直径为 3 的径向摩尔图中的界限

径向摩尔图保留了摩尔图的有序性和规则性，允许某些顶点具有比摩尔图更大的偏心率。对它们与摩尔图的相似性进行分类的一种方法是状态度量。图的状态定义为所有有序顶点对的距离总和，等于维纳指数的两倍。偏心率最小的顶点称为中心顶点。在本文中，我们研究了径向摩尔图的最大中心顶点数和状态的上限。最后，我们提出了一个直径为 3 的径向摩尔图族，并推测它具有最大状态。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.