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Forcing Total Outer Independent Edge Geodetic Number of a Graph
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Forcing Total Outer Independent Edge Geodetic Number of a Graph
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Journal Article
Forcing Total Outer Independent Edge Geodetic Number of a Graph
2021
Overview
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 .
Publisher
IOP Publishing
