Limited Packing vs. Tuple Domination in Graphs

D.A. Mojdeh1, B. Samadi2, S.M. Hosseini Moghaddam3
1Department of Mathematics, University of Mazandaran, Babolsar, Iran
2 Department of Mathematics, Arak University, Arak, Iran
3Qom Azad University, Qom, Iran

Abstract

In this paper, we investigate the concepts of \(k\)-limited packing and \(k\)-tuple domination in graphs and give several bounds on the size of them. These bounds involve many well-known parameters of graphs. Also, we establish a connection between these concepts that implies some new results in this area. Finally, we improve many bounds in the literature.