Abstract
The packing chromatic number $\raisebox{2pt}{$\chi$}_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi:V(G)\longrightarrow \{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. It is a frequency assignment problem used in wireless networks, which is also called broadcast coloring. It is proved that packing coloring is NP-complete for general graphs and even for trees. In this paper, we compute the packing chromatic number for circular fans with two and four chords and mesh of trees.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: International Journal of Mathematics and Soft Computing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.