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.