- Published 2013

Let G = (V,E) be a graph with p vertices and q edges. An acyclic graphoidal cover of G is a collection ψ of paths in G which are internally-disjoint and cover each edge of the graph exactly once. Let f : V → {1, 2, . . . , p} 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 ψf 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 ηl = min{|ψf | : f is a graphoidal labeling of G} is called the label graphoidal covering number of G. In this paper we characterize graphs for which (i) ηl = q −m, where m is the number of vertices of degree 2 and (ii) ηl = q. Also, we determine the value of label graphoidal covering number for unicyclic graphs.

@inproceedings{Rezaie2013OnLG,
title={On Label Graphoidal Covering Number-i},
author={Behruz Tayfeh Rezaie and Ayyappan Anitha},
year={2013}
}