Weighted graphs: Eigenvalues and chromatic number
Abstract
We revisit Hoffman relation involving chromatic number $\chi$ and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues $\lambda$ dan $\mu$ satisfy $\lambda=(1-\chi)\mu.$ We study in particular the eigenvalues of the integer simplex $T_m^2,$ a 3-chromatic graph on $\binom {m+2}{2}$ vertices.
Keywords
graph spectra; chromatic number
Full Text:
PDFDOI: http://dx.doi.org/10.5614/ejgta.2016.4.1.2
Refbacks
- There are currently no refbacks.
ISSN: 2338-2287
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.<div class="statcounter"><a title="web analytics" href="http://statcounter.com/" target="_blank"><img class="statcounter" src="//c.statcounter.com/11284516/0/7b1b10eb/1/" alt="web analytics"></a></div>