Abstract:A path covering of a graph G is a set of vertex disjoint paths of G containing all the vertices of G. The path covering number of G, denoted by P (G), is the minimum number of paths in a path covering ofThe L(2, 1)-labeling number λ(G) of G is the smallest number k such that G has a k-L(2, 1)-labeling. The purpose of this paper is to study path covering number and L(2, 1)-labeling number of graphs. Our main work extends most of results in [On island sequences of labelings with a condition at distance two, Disc… Show more
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