The Eigenvalues of the Graphs $D(4,q)$
| العنوان: | The Eigenvalues of the Graphs $D(4,q)$ |
|---|---|
| المؤلفون: | G. Eric Moorhouse, Jason Williford, Shuying Sun |
| سنة النشر: | 2017 |
| مصطلحات موضوعية: | Connected component, Cayley graph, 010102 general mathematics, 0102 computer and information sciences, 01 natural sciences, Graph, Theoretical Computer Science, Ramanujan's sum, Combinatorics, symbols.namesake, Computational Theory and Mathematics, 010201 computation theory & mathematics, Bounded function, FOS: Mathematics, symbols, Discrete Mathematics and Combinatorics, Expander graph, Mathematics - Combinatorics, Combinatorics (math.CO), 0101 mathematics, 05C50, 05C25, Prime power, Eigenvalues and eigenvectors, Mathematics |
| الوصف: | The graphs D ( k , q ) have connected components C D ( k , q ) giving the best known bounds on extremal problems with forbidden even cycles, and are denser than the well-known graphs of Lubotzky, Phillips, Sarnak [14] and Margulis [15] , [16] . Despite this, little is known about the spectrum and expansion properties of these graphs. In this paper we find the spectrum for k = 4 , the smallest open case. For each prime power q, the graph D ( 4 , q ) is q-regular graph on 2 q 4 vertices, all of whose eigenvalues other than ±q are bounded in absolute value by 2 q . Accordingly, these graphs are good expanders, in fact very close to Ramanujan . |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4b8254bfd0409f0f788b36085588bdfa http://arxiv.org/abs/1701.03685 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....4b8254bfd0409f0f788b36085588bdfa |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |