Extremal Edge General Position Sets in Some Graphs

A set of edges X⊆ 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 gp_e(G) of G is the cardinality of a largest edge general position set in G. Graphs G with gp_e(G) = |E(G)| - 1 and with gp_e(G) = 3 are respectively characterized. Sharp upper and lower bounds on gp_e(G) are proved for block graphs G and exact values are determined for several specific block graphs.