• GEODESIC 2-GRAPHOIDAL COVERING NUMBER OF A BICYCLIC GRAPHS

Abstract

A geodesic 2-graphoidal cover of a graph G is a collection  of shortest paths in G such that every path in  has at least two vertices, every vertex of G is an internal vertex of at most two paths in  and every edge of G is in exactly one path in . The minimum cardinality of a geodesic 2- graphoidal cover of G is called the geodesic 2-graphoidal covering number of G and is denoted by . In this paper we determine  for bicyclic graphs.