给定阶边环图的最小尺寸和最大直径

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-05-16 DOI:10.1016/j.disc.2025.114576

Chengli Li, Feng Liu, Xingzhi Zhan

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引用次数: 0

摘要

图中的k环是一个长度为k的环。如果对于3≤k≤n的每一个整数k， G的每条边都在k环中，则称图G为n阶的边环。给出了给定阶的简单边环图的最小尺寸的下界和上界，并确定了这种图的最大直径。在3连接的情况下，确定了精确的最小尺寸。我们还确定了给定顺序的图的最小尺寸，其中每个边都位于三角形中。

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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The minimum size and maximum diameter of an edge-pancyclic graph of a given order

A k-cycle in a graph is a cycle of length k. A graph G of order n is called edge-pancyclic if for every integer k with

3 \leq k \leq n

, every edge of G lies in a k-cycle. We give lower and upper bounds on the minimum size of a simple edge-pancyclic graph of a given order, and determine the maximum diameter of such a graph. In the 3-connected case, the precise minimum size is determined. We also determine the minimum size of a graph of a given order with connectivity conditions in which every edge lies in a triangle.

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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.