๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Ramanujan Edge-Indexed Graphs

โœ Scribed by Shahriar Mokhtari-Sharghi


Book ID
102584390
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
362 KB
Volume
81
Category
Article
ISSN
0095-8956

No coin nor oath required. For personal study only.

โœฆ Synopsis


In this paper I study the spectrum of edge-indexed graphs. For any k, an explicit infinite family of k-regular finite Ramanujan edge-indexed graphs is given. Conditions for the grouping of this family are provided; fulfilling them would lead to an infinite family of k-regular Ramanujan graphs.


๐Ÿ“œ SIMILAR VOLUMES


Ramanujan graphs
โœ A. Lubotzky; R. Phillips; P. Sarnak ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› Springer-Verlag ๐ŸŒ English โš– 763 KB
Cubic Ramanujan graphs
โœ Patrick Chiu ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Springer-Verlag ๐ŸŒ English โš– 516 KB
Finite Euclidean graphs and Ramanujan gr
โœ Eiichi Bannai; Osamu Shimabukuro; Hajime Tanaka ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 530 KB
Ramanujan Graphs with Small Girth
โœ Yair Glasner ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Springer-Verlag ๐ŸŒ English โš– 250 KB
Finite Fields and Ramanujan Graphs
โœ J Arias de Reyna ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 276 KB

We give a new method to construct Ramanujan graphs and apply it to define two new families of Ramanujan graphs. These new graphs have a very easy description and we prove that they are Ramanujan graphs in an elementary way.