On the packing numbers in graphs

D. A. Mojdeh; B. Samadi; A. Khodkar; H. R. Golmohammadi

On the packing numbers in graphs

Combinatorics 2019-08-27 v1

Authors: D. A. Mojdeh , B. Samadi , A. Khodkar , H. R. Golmohammadi

Abstract

In this paper, we find upper bounds on the open packing and $k$ -limited packing numbers with emphasis on the cases $k=1$ and $k=2$ . We solve the problem of characterizing all connected graphs on $n$ vertices with $\rho_{o}(G)=n/\delta(G)$ which was presented in 2015 by Hamid and Saravanakumar. Also, by establishing a relation between the $k$ -limited packing number and double domination number we improve two upper bounds given by Chellali and Haynes in 2005.

Keywords

graph pebbling graph theory hypergraph theory

Cite

@article{arxiv.1707.08656,
  title  = {On the packing numbers in graphs},
  author = {D. A. Mojdeh and B. Samadi and A. Khodkar and H. R. Golmohammadi},
  journal= {arXiv preprint arXiv:1707.08656},
  year   = {2019}
}