Finite Fields and Ramanujan Graphs
β Scribed by J Arias de Reyna
- Book ID
- 102588714
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 276 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
We generalize the construction of F. R. Chung of graphs from finite fields and estimate their parameters with the help of a new bound of exponential sums due to G. I. Perel'muter and the author.
Let G be a graph, let R be a finite field and F a subgroup of the automorphism group Aut G of G. For a labeling of the vertices of G with elements of R, we consider labelings of the edges of G with elements of R such that the label on each edge is equal to the sum of labels on the two incident verti