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.
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 in
G
. The cardinality of a largest edge general position set of
G
is ...the edge general position number of
G
. In this paper, edge general position sets are investigated in partial cubes. In particular, it is proved that the union of two largest
Θ
-classes of a Fibonacci cube or a Lucas cube is a maximal edge general position set.
