Combinatorial and spectral properties of König-Egerváry graphs

Some combinatorial and spectral properties of König-Egerváry (K-E) graphs are presented. In particular, some new combinatorial characterizations of K-E graphs are introduced, the Laplacian spectrum of particular families of K-E graphs is deduced, and a lower and upper bound on the largest and smallest adjacency eigenvalue, respectively, of a K-E graph are determined.