Weighted Graphs: Eigenvalues and Chromatic Number
2016  //  DOI: 10.5614/ejgta.2016.4.1.2
Charles Delorme

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Weighted Graphs: Eigenvalues and Chromatic Number Image
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.

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  • Eye Icon 195 views
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Metrics Icon 195 views  //  78 downloads