## Mojdeh, Doost Ali and Peterin, Iztok and Samadi, Babak and Yero, Ismael G. - (Open) packing number of some graph products

dmtcs:5100 - Discrete Mathematics & Theoretical Computer Science, August 27, 2020, vol. 22 no. 4 - https://doi.org/10.23638/DMTCS-22-4-1
(Open) packing number of some graph products

Authors: Mojdeh, Doost Ali and Peterin, Iztok and Samadi, Babak and Yero, Ismael G.

The packing number of a graph $G$ is the maximum number of closed neighborhoods of vertices in $G$ with pairwise empty intersections. Similarly, the open packing number of $G$ is the maximum number of open neighborhoods in $G$ with pairwise empty intersections. We consider the packing and open packing numbers on graph products. In particular we give a complete solution with respect to some properties of factors in the case of lexicographic and rooted products. For Cartesian, strong and direct products, we present several lower and upper bounds on these parameters.

Volume: vol. 22 no. 4
Section: Graph Theory
Published on: August 27, 2020
Submitted on: January 23, 2019
Keywords: Mathematics - Combinatorics,05C69, 05C76