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Friendship-Like Graphs and It’s Classiffication

  • K. Nageswara RaoEmail author
  • P. Shaini
  • K. A. Germina
Conference paper
  • 51 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 307)

Abstract

A distance-compatible set-labeling (dcsl) of a connected graph G is an injective set assignment \(f : V(G) \rightarrow 2^{X},\) X being a nonempty set, such that the corresponding induced function \(f^{\oplus } :V(G)\times V(G) \rightarrow 2^{X}\) given by \(f^{\oplus }(uv)= f(u)\oplus f(v)\) satisfies \(\mid f^{\oplus }(uv) \mid = k_{(u,v)}^{f}d_{G}(u,v) \) for every pair of distinct vertices \(u, v \in V(G),\) where \(d_{G}(u,v)\) denotes the usual path distance between u and v and \(k_{(u,v)}^{f}\) is a constant. A dcsl f of G is k-uniform if all the constant of proportionality with respect to f are equal to k,  and if G admits such a dcsl then G is called a k-uniform dcsl graph. And it has been already proved that, for a finite graph G, k-uniform dcsl graph G with is a finite set X if and only if k-embedding of G into a hypercube \({\mathbf {H}}(X)\). In this paper, we introduce Friendship-like graphs and its classification and prove that it admits 2-uniform dcsl.

Keywords

k-Uniform dcsl graphs \(\lambda \)-Scale embeddable Friendship graphs 

Notes

Acknowledgements

The authors are thankful to the Department of Science and Technology, Government of India, New Delhi, for the financial support concerning the Major Research Project (Ref: No. SR/S4/MS : 760/12).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsMai Nefhi College of Science (EIT)HimbrtiEritrea
  2. 2.Department of Mathematics, School of Physical SciencesCentral University of KeralaKasaragodeIndia

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