Abstract
AbstractThe 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.
Funder
Science and Engineering Research Board India
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference32 articles.
1. Alon, N.: Eigenvalues and expanders. Combinatorica 8(2), 83–96 (1986)
2. Babai, L.: Group, graphs, algorithms: the graph isomorphism problem. In: Proceedings of the International Congress of Mathematicians, pp. 3303–3320 (2018)
3. Baldoni, M.W., Ciliberto, C., Cattaneo, G.M.P.: Elementary Number Theory, Cryptography and Codes. Springer, New York (2009)
4. Ballantine, C., Ciubotaru, D.: Ramanujan bigraphs associated with $$SU(3)$$ over a $$p$$-adic field. Proc Am Math Soc 139(6), 1939–1953 (2011)
5. Ballantine, C., Feigon, B., Ganapathy, R., Kool, J., Maurischat, K., Wooding, A.: Explicit construction of Ramanujan bigraphs. In: Women in Numbers in Europe, pp. 1–16. Springer (2015)
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