Please use this identifier to cite or link to this item: https://idr.l3.nitk.ac.in/jspui/handle/123456789/12362
Title: On k-graceful digraphs
Authors: Hegde, S.M.
Shivarajkumar
Issue Date: 2014
Citation: Utilitas Mathematica, 2014, Vol.95, , pp.161-173
Abstract: In this paper we extend the idea of k-graceful labeling of undirected graphs to a directed graphs: A simple directed graph D with n vertices and e edges is labeled by assigning each vertex a distinct element from the set ?c+k = {0,1,2.....e + k - 1}, where is a positive integer and an edge xy from vertex x to vertex y is labeled with ?(x, y) = ?(y) - ?(x)mod(e + k), where ?(y) and ?(x) are the values assigned to the vertices y and x respectively. A labeling is a k-graceful labeling if all ?(x, y) are distinct and belong to {k, k + 1,k + e-1}. If a digraph D admits a k-graceful labeling then D is a fc - graceful digraph. We also provide a list of values of fc for which the unidirectional cycle C?n admits a k-graceful labeling. Further, we give a necessary and sufficient condition for the outspoken unicyclic wheel to be k-graceful and prove that to provide a list of values of k > 1, for which the unicyclic wheel W?n is fc-graceful is NP - complete.
URI: http://idr.nitk.ac.in/jspui/handle/123456789/12362
Appears in Collections:1. Journal Articles

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