7.6.2019 10:00 @ Applied Mathematical Logic
In this talk we present new results on the partial sum of eigenvalues of the two main matrices in SGT: adjacency and Laplacian. Given a matrix M with eigenvalues $lambda_1geq lambda_2 geq ldotsgeq lambda_n$. We define the partial sum $S_k(M)=sum_{i=1}^klambda_i$ for $1leq kleq n$. This parameter has its origens in theoretical chemistry in the H"{u}ckel molecular orbital theory. In this theory the behavior of the so-called $pi$-electrons in an unsaturated conjugated molecule is fully described in terms of the eigenvalues of the corresponding adjacency matrix. This parameter has been extensively investigated for several different matrices. Here, we present new upper bounds for $S_k$ for the Laplacian and adjacency matrix of random graphs.
