DefinePK

Abstract

A decomposition of a graph G is a collection Ψ of edge-disjoint subgraphs of G such that every edge of G belongs to exactly one Hi. If each Hi is a path in G, then Ψ is called a path partition or path cover or path decomposition of G. A divisor path decomposition of a graph G is a path cover Ψ of G such that the length of all the paths in Ψ 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 πD(G). In this paper, we initiate a study of the parameter πD and determine the value of πD for some standard graphs. Further, we obtain some bounds for πD and characterize graphs attaining the bounds.