Shivaramakrishna Pragada

Let $G$ be a graph with $n$ vertices. Let $A(G)$ be its adjacency matrix. Let $\lambda_1(G), \lambda_2(G)$ denote the largest and second largest eigenvalues of the adjacency matrix. Bollob\'{a}s and Nikiforov (2007) conjectured that for any graph $G...

In this talk, we investigate the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. We show that the eigenvalues of the sequences of graphs obtained by subdividing edges are Cauchy. As an application...