Extremal Edge General Position Sets in Some Graphs

A set of edges X⊆ E(G) 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 gpₑ(G) 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 gp e ( G ) = | E ( G ) | - 1 and with gp_e(G) = 3 gp e ( G ) = 3 are respectively characterized. Sharp upper and lower bounds on gp_e(G) gp e ( G ) are proved for block graphs G and exact values are determined for several specific block graphs.