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
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)