In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal ...

The complete graph Kr as well as the bipartite graph Kr,r are easily seen to be Ramanujan (see the discussion in section 2). The Petersen graph (see Figure. 1) ...

Abstract. We give a short survey of the theory of Ramanujan graphs. Beginning with basic notions, we introduce Cayley graphs and describe how.

6 дней назад · An (n, k, λ)-graph Γ is called a Ramanujan graph if λ ≤ 2 √ k − 1 [1, 11] . It is well known that Ramanujan graphs are expander graphs [11]. ...

There are two ways to construct relatively small Ramanujan graph: the random way and the deterministic way. In this paper, the deterministic methods for ...

25 дек. 2014 г. · In the Hoory, Linial, Wigderson survey (see Section 2.4 and Definition 5.11), a d-regular graph is called Ramanujan if the maximum absolute ... Explicit constructions of Ramanujan graphs - MathOverflow Ramanujan graphs from varieties over finite fields - MathOverflow Ramanujan graph element in $\mathsf{PSL}(2, \mathbb{Z}_q) Matching polynomials and Ramanujan graphs - MathOverflow Другие результаты с сайта mathoverflow.net

12 апр. 2016 г. · Abstract:The recent work by Marcus, Spielman and Srivastava proves the existence of bipartite Ramanujan (multi)graphs of all degrees and all ...

A Ramanujan graph is a connected regular graph whose second largest eigenvalue in absolute value is asymptotically the smallest possible. In fact, Ramanujan ...

1 февр. 2023 г. · We propose to interpret it through the lens of the Ramanujan Graph - a class of expander graphs that are sparse while being highly connected.