On the k-limited packing numbers in graphs

We give a sharp lower bound on the lower k-limited packing number of a general graph. Moreover, we establish a Nordhaus-Gaddum type bound on 2-limited packing number of a graph G of order n as L2(G)+L2(Ḡ)≤n+2. Also, we investigate the concepts of packing number (1-limited packing number) and open packing number in graphs with more details. In this way, by making use of the well-known result of Farber (1984) for strongly chordal graphs and its total version (2005) for trees we prove the new upper bound γ(G)≤(n−ℓ+δ′s)/(1+δ′) for every connected strongly chordal graph G of order n≥3 with ℓ pendant vertices and s support vertices, where δ′ is the minimum degree taken over all vertices that are not pendant vertices, and improve γt(T)≤(n+s)/2 for every tree T, that was first proved by Chellali and Haynes in 2004.