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Forcing Total Outer Independent Edge Geodetic Number of a Graph
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Abstract
In this paper we learn the new idea of forcing total outer independent edge geodetic number of a graph. Let G be a connected graph and R be a minimum total outer independent edge geodetic set of G. A subset L ⊆ R is known as a forcing subset for R if R is the unique minimum total outer independent edge geodetic set containing L. A forcing subset for R of minimum cardinality is a minimum forcing subset of R. The forcing total outer independent edge geodetic number of G denoted by
f
1
t
o
i
(G) is
f
1
t
o
i
(G) = min
{
f
1
t
o
i
(
R
)
}
, where the minimum is taken over all minimum total outer independent edge geodetic set R in G. Some general properties satisfied by this concept are studied. It is shown that for any couple of integers l, m with0 < l ≤ m − 4, there exists a connected graph G such that
f
1
t
o
i
(
G
)
=
l
and
g
1
t
o
i
(
G
)
=
m
.
Title: Forcing Total Outer Independent Edge Geodetic Number of a Graph
Description:
Abstract
In this paper we learn the new idea of forcing total outer independent edge geodetic number of a graph.
Let G be a connected graph and R be a minimum total outer independent edge geodetic set of G.
A subset L ⊆ R is known as a forcing subset for R if R is the unique minimum total outer independent edge geodetic set containing L.
A forcing subset for R of minimum cardinality is a minimum forcing subset of R.
The forcing total outer independent edge geodetic number of G denoted by
f
1
t
o
i
(G) is
f
1
t
o
i
(G) = min
{
f
1
t
o
i
(
R
)
}
, where the minimum is taken over all minimum total outer independent edge geodetic set R in G.
Some general properties satisfied by this concept are studied.
It is shown that for any couple of integers l, m with0 < l ≤ m − 4, there exists a connected graph G such that
f
1
t
o
i
(
G
)
=
l
and
g
1
t
o
i
(
G
)
=
m
.
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