Let G be a graph with two non adjacent vertices and G′ the graph constructed from G by adding an edge between them. It is known that the trace of Q′ is 2 plus the trace of Q, where Q and Q′ are the… (More)

The original graph sandwich problem for a property Π, as defined by Golumbic, Kaplan, and Shamir, can be stated as follows: given two graphs G1 = (V,E1) and G2 = (V,E2), is there a graph G = (V,E)… (More)

Cographs have always been a research target in areas such as coloring, graph decomposition, and spectral theory. In this work, we present an algorithm to generate all unlabeled cographs with n… (More)

Celso Marques da Silva Junior, Celso Suckow da Fonseca, +4 authorsRenata R. Del-Vecchio

2017

In this note, the graphs of order n having the largest distance Laplacian eigenvalue of multiplicity n− 2 are characterized. In particular, it is shown that if the largest eigenvalue of the distance… (More)

Let G be a simple graph and L = L(G) the Laplacian matrix of G. G is called L-integral if all its Laplacian eigenvalues are integer numbers. It is known that every cograph, a graph free of P4, is… (More)

Let G be a graph formed by connecting a tree and a threshold graph with an edge between their respective roots. Let A be the adjacency matrix of G and x ∈ R. We give an O(n) algorithm for… (More)