Ramanujan graphs arising as weighted Galois covering graphs
We give a new construction of Ramanujan graphs using a generalized type of covering graph called a weighted covering graph. For a given prime p the basic construction produces bipartite Ramanujan graphs with 4p vertices and degrees 2N where roughly $p + 1 - \sqrt{2p} < N \le p$. We then give gene...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2018-04-03.
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| LEADER | 02192 am a22002533u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_264_pdf_69 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Minei, Marvin; Pacific Missile Range Facility, Department of Navy, Barking Sands, HI 96752. |e author |
| 100 | 1 | 0 | |a Marvin Minei |e contributor |
| 700 | 1 | 0 | |a Skogman, Howard; Department of Mathematics, College at Brockport, SUNY, Brockport, NY 14420. |e author |
| 245 | 0 | 0 | |a Ramanujan graphs arising as weighted Galois covering graphs |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2018-04-03. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/264 | ||
| 520 | |a We give a new construction of Ramanujan graphs using a generalized type of covering graph called a weighted covering graph. For a given prime p the basic construction produces bipartite Ramanujan graphs with 4p vertices and degrees 2N where roughly $p + 1 - \sqrt{2p} < N \le p$. We then give generalizations to produce Ramanujan graphs of other sizes and degrees as well as general results about base graphs which have weighted covers that satisfy their Ramanujan bounds. To do the construction, we define weighted covering graphs and distinguish a subclass of Galois weighted covers that allows for block diagonalization of the adjacency matrix. The specific construction allows for easy computation of the resulting blocks. The Gershgorin Circle Theorem is then used to compute the Ramanujan bounds on the spectra. | ||
| 540 | |a Copyright (c) 2018 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a Ramanujan graphs, covering graphs, weighted graphs, Galois covers, block diagonalization, graph spectra | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications; 123-137 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/264/pdf_69 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/264/pdf_69 |z Get Fulltext |