Improved lower bounds on the extrema of eigenvalues of graphs
Abstract
In this note, we improve the lower bounds for the maximum size of the kth largest eigenvalue of the adjacency matrix of a graph for several values of k. In particular, we show that closed blowups of the icosahedral graph improve the lower bound for the maximum size of the fourth largest eigenvalue of a graph, answering a question of Nikiforov.
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