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.

中文翻译：

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一些图中的极值边一般位置集

摘要

如果X中没有三个边位于公共最短路径上，则图G的边集\(X\subseteq E(G)\)是边一般位置集。 G 的边总位置数\({\textrm{gp}}_{ \ textrm{e}}(G)\)是G中最大的边总位置集合的基数。图形G具有\({\textrm{gp}}_{{\textrm{e}}}(G) = |E(G)| - 1\)和\({\textrm{gp}}_{{ \textrm{e}}}(G) = 3\)分别进行表征。证明了块图 G的 \({\textrm{gp}}_{{\textrm{e}}}(G)\)上的尖锐上下界，并为几个特定的​​块图确定了精确值。