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Graceful Labeling of Bow Graphs and Shell-Flower Graphs

J. Jeba Jesintha,Ezhilarasi Hilda Stanley

Published in:   Vol. 2 Issue 1 Date of Publication:   June 2013
Page(s):   62-64 Publisher:   Integrated Intelligent Research (IIR)
DOI:   10.20894/IJCOA. SAI : 2013SCIA316F0963

A graceful labeling of a graph G with �q� edges and vertex set V is an injection f: V(G) → {0,1,2,�.q} with the property that the resulting edge labels are also distinct, where an edge incident with vertices u and v is assigned the label |f(u) � f(v)| . A graph which admits a graceful labeling is called a graceful graph. A Shell graph is defined as a cycle Cnwith (n -3) chords sharing a common end point called the apex . Shell graphs are denoted as C(n, n- 3). A multiple shell is defined to be a collection of edge disjoint shells that have their apex in common. Hence a double shell consists of two edge disjoint shells with a common apex. A bow graph is defined to be a double shell in which each shell has any order. In this paper we prove that the bow graph with shell orders �m� and �2m� is graceful. Further in this paper we define a shell � flower graph as k copies of [C(n, n-3) U K2] and we prove that all shell - flower graphs are graceful for n = 4.