On friendly index set of graphs

M. Teffilia¹ , J. Devaraj²

Section:Review Paper, Product Type: Isroset-Journal
Vol.5 , Issue.4 , pp.258-263, Aug-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.258263

Online published on Aug 31, 2018

Copyright © M. Teffilia, J. Devaraj . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
A function f from V(G) to {0,1} where for each edge xy ,f*(xy) = (f(x) +f(y))(mod2), let vi(f) is the number of vertices v with f(v) = i and ei(f) is the number of edges e with f*(e) = i is called friendly if |v0(f) - v1(f)| ≤ 1. The friendly index set of a graph G is FI(G) = {|e0(f) - e1(f)|, where f runs over all friendly labelings f of G}. In this paper we find the friendly index set of the umbrella graph, Spl(K1,n), Globe graph ,P2+mk1 and union of a path and a star sharing a vertex in common.

Key-Words / Index Term :
Friendly labeling, Friendly index set, Umbrella graph, Spl(K1,n), Globe graph

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