%0 Journal Article
%T Butterfly Graphs with Shell Orders m and 2m+1 are Graceful
%A Ezhilarasi Hilda Stanley
%J Bonfring International Journal of Research in Communication Engineering
%D 2012
%I Bonfring
%R 10.9756/bijrce.1245
%X A graceful labelling of an un directed graph G with n edges is a one-one function from the set of vertices V(G) to the set {0, 1, ,2, . . ., n} such that the induced edge labels are all distinct. An induced edge label is the absolute difference between the two end vertex labels. A shell graph is defined as a cycle Cn with (n -3) chords sharing a common end point called the apex . A double shell is one vertex union of two shells. A bow graph is defined to be a double shell in which each shell has any order. In this paper we define a butterfly graph as a bow graph with exactly two pendant edges at the apex and we prove that all butterfly graphs with one shell of order m and the other shell of order (2m + 1) are graceful.
%K Bow Graph
%K Butterfly Graph
%K Graceful Labelling
%K Shell Graph
%U http://www.journal.bonfring.org/papers/rce/volume2/BIJ-002-1245.pdf