Please use this identifier to cite or link to this item: https://idr.l4.nitk.ac.in/jspui/handle/123456789/10366
Title: Construction of graceful digraphs using algebraic structures
Authors: Hegde, S.M.
Kumudakshi
Issue Date: 2016
Citation: Journal of Discrete Mathematical Sciences and Cryptography, 2016, Vol.19, 1, pp.103-116
Abstract: Abstract: In the early 1980?s Bloom and Hsu extended the notation of graceful labelings to directed graphs, and gave a relationship between graceful digraphs and a variety of algebraic structures. In this paper using a cyclic (v, k, ?) difference set with ? copies of elements of Zv\ {0}, we construct graceful digraphs of k vertices and v 1 arcs. It is known that if gracefully labelled graph has e edges then its symmetric digraph is graceful with the same vertex labels. Although, the cycle Cm is not graceful for m?1, 2 (mod 4) we show that the symmetric digraph based on cycle Cm i.e the double cycle, DCm which is constructed from a m-cycle by replacing each edge by a pair of arcs, edge xy gives rise to arcs (x, y) and (y, x), is graceful for any m vertices specifically for m?1, 2 (mod 4). 2016 TARU Publications.
URI: http://idr.nitk.ac.in/jspui/handle/123456789/10366
Appears in Collections:1. Journal Articles

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