Butterfly Graphs with Shell Orders m and 2m+1 are Graceful
Ezhilarasi Hilda Stanley · Bonfring International Journal of Research in Communication Engineering · 2012
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.