Fat Hoffman graphs with smallest eigenvalue at least −1 − τ
DOI:
https://doi.org/10.26493/1855-3974.287.137Keywords:
Hoffman graph, line graph, graph eigenvalue, special graphAbstract
In this paper, we show that all fat Hoffman graphs with smallest eigenvalue at least − 1 − τ, where τ is the golden ratio, can be described by a finite set of fat (− 1 − τ)-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mean that every fat Hoffman graph with smallest eigenvalue at least − 1 − τ is an H-line graph, where H is the set of isomorphism classes of maximal fat (− 1 − τ)-irreducible Hoffman graphs. It turns out that there are 37 fat (− 1 − τ)-irreducible Hoffman graphs, up to isomorphism.
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Published
2013-04-22
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Section
Special Issue Bled'11
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Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/