Decomposition of Bicyclic graphs into Paths and Cycles

This paper deals with the decomposition of three types of bicyclicgraphs into paths and cycles using a 2-simple graphoidal cover(2-simple gc). A 2-simple graphoidal covering of a graph H is a set ψa ofpaths in H such that every edge is in exactly one path in ψa, everyvertex is an internal vertex of at most two paths and any two pathsin ψa have at most one vertex in common. The minimum cardinalityof 2-simple graphoidal cover ψa of H is known as 2-simple graphoidalcovering number of H, denoted by η2s. Mathematics Subject Classification (2010). Primary 05C70; Secondary 05C38.