The objectives of this article are threefold. Firstly, we present for the first time explicit constructions of an infinite family of unbalanced Ramanujan bigraphs. Secondly, we revisit some of the known methods for constructing Ramanujan graphs and discuss the computational work required in actually implementing the various construction methods. The third goal of this article is to address the following question: can we construct a bipartite Ramanujan graph with specified degrees, but with the restriction that the edge set of this graph must be distinct from a given set of “prohibited” edges? We provide an affirmative answer in many cases, as long as the set of prohibited edges is not too large.

本文的目标是三个方面。首先，我们首次提出了一个不平衡的拉马努扬传记集的无穷家族的显式构造。其次，我们回顾一些构造Ramanujan图的已知方法，并讨论实际实现各种构造方法所需的计算工作。本文的第三个目标是解决以下问题：我们可以构造具有指定度数的二分拉曼努扬图，但有一个限制，即该图的边集必须与给定的“禁止”边集区分开吗？在许多情况下，只要禁止边缘的范围不太大，我们都会提供肯定的答案。