Extremal Edge General Position Sets in Some Graphs

IF 0.6 4区数学 Q3 MATHEMATICS

Graphs and Combinatorics Pub Date : 2024-03-26 DOI:10.1007/s00373-024-02770-z

引用次数: 0

Abstract

A set of edges \(X\subseteq E(G)\) of a graph G is an edge general position set if no three edges from X lie on a common shortest path. The edge general position number \({\textrm{gp}}_{\textrm{e}}(G)\) of G is the cardinality of a largest edge general position set in G. Graphs G with \({\textrm{gp}}_{{\textrm{e}}}(G) = |E(G)| - 1\) and with \({\textrm{gp}}_{{\textrm{e}}}(G) = 3\) are respectively characterized. Sharp upper and lower bounds on \({\textrm{gp}}_{{\textrm{e}}}(G)\) are proved for block graphs G and exact values are determined for several specific block graphs.

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某些图中的极边一般位置集

Abstract 如果没有来自 X 的三条边位于一条共同的最短路径上，那么图 G 的边集 \(X\subseteq E(G)\)就是一个边一般位置集。G 的边一般位置数（{\textrm{gp}}_{\textrm{e}}(G)\）是 G 中最大的一个边一般位置集的卡入度。分别描述了具有 \({\textrm{gp}}_{{\textrm{e}}(G) = |E(G)| - 1\) 和 \({\textrm{gp}}_{{\textrm{e}}(G) = 3\) 的图 G。对于块图 G，证明了 \({\textrm{gp}}_{\textrm{e}}}(G)\)的尖锐上界和下界，并确定了几个特定块图的精确值。

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

Graphs and Combinatorics 数学-数学

CiteScore

1.00

自引率

14.30%

发文量

160

审稿时长

6 months

期刊介绍： Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.