Advertisement
Published in:
2020 | OriginalPaper | Chapter
Friendship-Like Graphs and It’s Classiffication
Authors : K. Nageswara Rao, P. Shaini, K. A. Germina
Published in: Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory
Publisher: Springer Singapore
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.