AN ELABORATE STUDY OF GRAPHOIDAL COVERING NUMBER OF A GRAPH

A Graphoidal cover of a graph G = (V,E) is a collection of paths in G such that (a) every path has at least two vertices (b) every vertex of G is an internal vertex of at most one path, and (c) every edge of G is in some path. The graphoidal covering number (G) of G is defined to be the minimum cardinality of a graphoidal cover of G. In this thesis we determine the graphoidal covering numbers of trees, complete bipartrite graphs. Hamiltonian graphs and regular graphs.