Browsing by Author "Kumudakshi, K."

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    Construction of graceful digraphs using algebraic structures
    (Taru Publications, 2016) Hegde, S.M.; Kumudakshi, K.
    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.
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    Further Results on Graceful Directed Graphs
    (Elsevier B.V., 2016) Hegde, S.M.; Kumudakshi, K.
    In this paper we present the gracefulness of the directed graph Pm?Pn? which is an orientation of the planar grid graph Pm?Pn, in which each cell is a unicycle of length four. © 2016 Elsevier B.V.
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    Graceful digraphs and complete mappings
    (Elsevier B.V., 2015) Hegde, S.M.; Kumudakshi, K.
    Bloom and Hsu while extending the graceful labelings of graphs to digraphs, specified the relation between graceful unicycles and complete mappings by establishing the relation of each to a particular class of permutations. We denote C?m(r;m) as a digraph with two directed cycles, one with vertices v1,v2,. . .,vr-1,vr,vr+1,. . .,vm and another directed cycle with vertices v1,v21,. . .,vr-11,vr,vr+11,. . .,vm1 of same length, such that both the directed cycles have v1 and vr as the two common vertices (where m ? 4, 3 ? r ? m-1). In this paper we use complete mappings to deduce a partition of Zn, where n=2m+1 odd and show that the digraph C?m(r;m) is graceful. © 2015 Elsevier B.V.