Friendship-Like Graphs and It’s Classiffication

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


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.


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



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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© 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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