ON LABEL GRAPHOIDAL COVERING NUMBER-I

Let G = (V;E) be a graph with p vertices and q edges. An acyclic graphoidal cover of G is a collection of paths in G which are internally-disjoint and cover each edge of the graph exactly once. Let f : V ! f1; 2; : : : ; pg be a bijective labeling of the vertices of G. Let " Gf be the directed graph obtained by orienting the edges uv of G from u to v provided f(u) < f(v). If the set f of all maximal directed paths in " Gf , with directions ignored, is an acyclic graphoidal cover of G, then f is called a graphoidal labeling of G and G is called a label graphoidal graph and l = minfj f j : f is a graphoidal labeling of Gg is called the label graphoidal covering number of G. In this paper we characterize graphs for which (i) l = q ?? m, where m is the number of vertices of degree 2 and (ii) l = q. Also, we determine the value of label graphoidal covering number for unicyclic graphs.