The second largest eigenvalue of a graph (A survey)


Dragoš Cvetković, Slobodan Simić




This is a survey paper on the second largest eigenvalue A2 of the adjacency matrix of a graph. Among the topics presented are the graphs with small $\apha_2$, bounds for $\apha_2$, algebraic connectivity, graphs with good expanding properties (such as Ramanujan graphs), rapidly mixing Markov chains etc. Applications to computer science are mentioned. Recent results of the authors are included.