某些图中的极边一般位置集

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

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引用次数: 0

摘要

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。

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Extremal Edge General Position Sets in Some Graphs

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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