ON TOPOLOGICAL INTEGER ADDITIVE SET-LABELING OF GRAPHS



Authors

  • Udayan Prajapati1, Karan Odedara2

DOI:

https://doi.org/10.15282/jmes.17.1.2023.10.0759


Keywords:

set-labeling, integer additive set-labeling, topological integer additive set-labeling, graphs


Abstract

Extending the concepts of IASL and topological set-labeling, Sudev and Germina have introduced TIASL in 2015. For a graph G and a non-empty set S, a TIASL is defined as a mapping ψ∶ V(G)→P(S)∖{ϕ} such that ψ is one-one, the function induced ψ∶ E(G)→P(S) given by ψ^+ (uv) =ψ(u) +ψ(v) is well-defined (where the operation `+' between two sets is defined as sumset of two sets) and ψ(V(G))∪{ϕ} is a topology on S. The set S used here is known as ground set. In this paper, we give necessary and sufficient conditions for the given graph to admit TIASL with given non-empty set as a ground set. We also discuss embedding of graphs into TIASL graphs. We also give a formula to find topological set-labeling numbers of TIASL graphs.



Published

2024-04-08

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