Definition
Let be a connected -regular graph with vertices, and let be the eigenvalues of the adjacency matrix of . Because is connected and -regular, its eigenvalues satisfy . Whenever there exists with, define
A -regular graph is a Ramanujan graph if is defined and .
A Ramanujan graph is characterized as a regular graph whose Ihara zeta function satisfies an analogue of the Riemann Hypothesis.
Read more about this topic: Ramanujan Graph
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