Article ID Journal Published Year Pages File Type
4657144 Journal of Combinatorial Theory, Series B 2009 8 Pages PDF
Abstract

Let k be a positive integer and let G be a graph of order n⩾k. It is proved that the sum of k largest eigenvalues of G is at most . This bound is shown to be best possible in the sense that for every k there exist graphs whose sum is . A generalization to arbitrary symmetric matrices is given.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics