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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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