Extremal Edge General Position Sets in Some Graphs

Abstract 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 gp₄ (G) gp e (G) of G is the cardinality of a largest edge general position set in G. Graphs G with gp₄ (G) = |E (G) | - 1 gp e (G) = | E (G) | - 1 and with gp₄ (G) = 3 gp e (G) = 3 are respectively characterized. Sharp upper and lower bounds on gp₄ (G) gp e (G) are proved for block graphs G and exact values are determined for several specific block graphs.