ON LABEL GRAPHOIDAL COVERING NUMBER-I

Let g = (v;e) be a graph with p vertices and q edges. an acyclic graphoidal coverof g is a collection of paths in g which are internally-disjoint and cover each edge of the graphexactly once. let f : v ! f1; 2; : : : ; pg be a bijective labeling of the vertices of g. let gf bethe directed graph obtained by orienting the edges uv of g from u to v provided f(u) < f(v). ifthe set f of all maximal directed paths in gf , with directions ignored, is an acyclic graphoidalcover of g, then f is called a graphoidal labeling of g and g is called a label graphoidal graph andl = 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 ofdegree 2 and (ii) l = q. also, we determine the value of label graphoidal covering number for unicyclicgraphs.