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Divisor path decomposition number of a graph.

Author(s)
K. Nagarajan Department of Mathematics, Sri S.R.N.M. College, Sattur – 626 203, Tamil Nadu, India
A. Nagarajan Department of Mathematics, V.O.C. College, Tuticorin – 628 008, Tamil Nadu, India
Abstract
A decomposition of a graph G is a collection Y of edge-disjoint subgraphs H1,H2,..,Hn of G such that every edge of G belongs to exactly one Hi. If each Hi is a path in G, then Y is called a path partition or path cover or path decomposition of G. A divisor path decomposition of a (p,q)-graph G is a path cover Y of G such that the length of all the paths in Y divides q. The minimum cardinality of a divisor path decomposition of G is called the divisor path decomposition number of G and is denoted by pD(G). In this paper, we initiate a study of the parameter pD and determine the value of pD for some standard graphs. Further, we obtain some bounds for pD and characterize graphs attaining the bounds.
Publication Details
Page(s) 1-12
DOI DOI not available
Published Journal: Journal of Prime Research in Mathematics, Volume: 6, Issue: 0, Year: 2010

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