Butterfly Graphs with Shell Orders m and 2m+1 are Graceful

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Butterfly Graphs with Shell Orders m and 2m+1 are Graceful

Journal Title: Bonfring International Journal of Research in Communication Engineering - Year 2012, Vol 2, Issue 2

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 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.

Authors and Affiliations

Ezhilarasi Hilda Stanley , Jeba Jesintha J

Keywords

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EP ID EP114736
DOI 10.9756/BIJRCE.1245
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