Abstract
AbstractA set of edges $$X\subseteq E(G)$$
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 $${\textrm{gp}}_{\textrm{e}}(G)$$
gp
e
(
G
)
of G is the cardinality of a largest edge general position set in G. Graphs G with $${\textrm{gp}}_{{\textrm{e}}}(G) = |E(G)| - 1$$
gp
e
(
G
)
=
|
E
(
G
)
|
-
1
and with $${\textrm{gp}}_{{\textrm{e}}}(G) = 3$$
gp
e
(
G
)
=
3
are respectively characterized. Sharp upper and lower bounds on $${\textrm{gp}}_{{\textrm{e}}}(G)$$
gp
e
(
G
)
are proved for block graphs G and exact values are determined for several specific block graphs.
Funder
Javna Agencija za Raziskovalno Dejavnost RS
TUBITAK
NNSF China
Publisher
Springer Science and Business Media LLC
Cited by
2 articles.
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