Discrete Mathematics, Algorithms and Applications, Volume (15), No (5), Year (2022-8)

Title : ( Equitable partition for some Ramanujan graphs )

Authors: M. ALINEJAD , Ahmad Erfanian , S. Fulad ,

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Abstract

For a d-regular graph G, an edge-signing σ:E(G)→{−1,1} is called a good signing if the absolute eigenvalues of its adjacency matrix are at most 2d−1−−−−√. Bilu and Linial conjectured that for each regular graph there exists a good signing. In this paper, by using the concept of “Equitable Partition”, we prove the conjecture for some cases. We show 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

, Edge signing, Good signing, Adjacency matrix, Lexicographic product.
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@article{paperid:1094233,
author = {M. ALINEJAD and Erfanian, Ahmad and S. Fulad},
title = {Equitable partition for some Ramanujan graphs},
journal = {Discrete Mathematics, Algorithms and Applications},
year = {2022},
volume = {15},
number = {5},
month = {August},
issn = {1793-8309},
keywords = {Edge signing; Good signing; Adjacency matrix; Lexicographic product.},
}

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%0 Journal Article
%T Equitable partition for some Ramanujan graphs
%A M. ALINEJAD
%A Erfanian, Ahmad
%A S. Fulad
%J Discrete Mathematics, Algorithms and Applications
%@ 1793-8309
%D 2022

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