Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Forcing Total Outer Independent Edge Geodetic Number of a Graph
View through CrossRef
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
.
Related Results
The upper connected edge geodetic number of a graph
The upper connected edge geodetic number of a graph
For a non-trivial connected graph G, a set S ? V (G) is called an edge
geodetic set of G if every edge of G is contained in a geodesic joining some
pair of vertices in S. The...
The edge-to-edge geodetic domination number of a graph
The edge-to-edge geodetic domination number of a graph
Let G = (V, E) be a connected graph with at least three vertices. A set S Í E is called an edge-to-edge geodetic dominating set of G if S is both an edge-to-edge geodetic set of G ...
Magic graphs
Magic graphs
DE LA TESIS<br/>Si un graf G admet un etiquetament super edge magic, aleshores G es diu que és un graf super edge màgic. La tesis està principalment enfocada a l'estudi del c...
THE FORCING EDGE FIXING EDGE-TO-VERTEX MONOPHONIC NUMBER OF A GRAPH
THE FORCING EDGE FIXING EDGE-TO-VERTEX MONOPHONIC NUMBER OF A GRAPH
For a connected graph G = (V, E), a set Se ⊆ E(G)–{e} is called an edge fixing edge-to-vertex monophonic set of an edge e of a connected graph G if every vertex of G lies on an e –...
Advances and Applications in Discrete Mathematics
Advances and Applications in Discrete Mathematics
A zero forcing set
in a graph
is called a dom-forcing set if
is also a dominating set of
. The minimum cardinality of such a set is known as the dom-forcing number of the gr...
Extreme Outer Connected Geodesic Graphs
Extreme Outer Connected Geodesic Graphs
For a connected graph G of order at least two, a set S of vertices in a graph G is said to be an outer connected geodetic set if S is a geodetic set of G and either S = V or the su...
Graph convolutional neural networks for 3D data analysis
Graph convolutional neural networks for 3D data analysis
(English) Deep Learning allows the extraction of complex features directly from raw input data, eliminating the need for hand-crafted features from the classical Machine Learning p...
Product of digraphs, (super) edge-magic valences and related problems
Product of digraphs, (super) edge-magic valences and related problems
Discrete Mathematics, and in particular Graph Theory, has gained a lot of popularity during the last 7 decades. Among the many branches in Graph Theory, graph labelings has experim...