Equitable partitions for Ramanajun graphs
Combinatorics
2021-08-03 v2
Abstract
For d-regular graph G, an edge-signing sigma:E(G) \rightarrow {-1,1} is called a good signing if the absolute eigenvalues of adjacency matrix are at most 2 \sqrt{d-1}. Bilu-Linial conjectured that for each regular graph there exists a good signing. In this paper, by using new concept "Equitable Partition", we solve the Bilu-Linial Conjecture for some cases. We show that how to find out a good signing for special complete graphs and lexicographic product of two graphs. In particular, if there exist two good signings for graph G, then we can find a good signing for a 2-lift of G.
Keywords
Cite
@article{arxiv.2107.11563,
title = {Equitable partitions for Ramanajun graphs},
author = {Mohsen Alinejad and Sanaz Fulad},
journal= {arXiv preprint arXiv:2107.11563},
year = {2021}
}