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Erschienen in:
2020 | OriginalPaper | Buchkapitel
Friendship-Like Graphs and It’s Classiffication
verfasst von : K. Nageswara Rao, P. Shaini, K. A. Germina
Erschienen in: Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory
Verlag: Springer Singapore
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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.