Bonfring International Journal of Research in Communication Engineering
Online ISSN: 2277-5080 | Print ISSN: 2250-110X | Frequency: 4 Issues/Year
Impact Factor: 0.528 | International Scientific Indexing(ISI) calculate based on International Citation Report(ICR)
Butterfly Graphs with Shell Orders m and 2m+1 are Graceful
Abstract:
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 orologi replica di lusso 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.
Keywords: Bow Graph, Butterfly Graph, Graceful Labelling, Shell Graph
Volume: 3 | Issue: 3
Pages: 11-15
Issue Date: September , 2013
DOI: 10.9756/BIJRCE.1245
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