On Q-spectral integral variation

Let G be a graph with two non adjacent vertices and G0 the graph constructed from G by adding an edge between them. It is known that the trace of Q0 is 2 plus the trace of Q, where Q and Q0 are the signless Laplacian matrices of G and G0 respectively. So, the sum of the Q0-eigenvalues of G0 is the sum of the the Q- eigenvalues of G plus two. It is said that Q-spectral integral variation occurs when either only one Q-eigenvalue is increased by two or two Q-eigenvalues are increased by 1 each one. In this article we present some conditions for the occurrence of Q-spectral integral variation under the addition of an edge to a graph G

On Q-spectral integral variation

Let G be a graph with two non adjacent vertices and G0 the graph constructed from G by adding an edge between them. It is known that the trace of Q0 is 2 plus the trace of Q, where Q and Q0 are the signless Laplacian matrices of G and G0 respectively. So, the sum of the Q0-eigenvalues of G0 is the sum of the the Q- eigenvalues of G plus two. It is said that Q-spectral integral variation occurs when either only one Q-eigenvalue is increased by two or two Q-eigenvalues are increased by 1 each one. In this article we present some conditions for the occurrence of Q-spectral integral variation under the addition of an edge to a graph G

Spectral characterizations of propeller graphs

A propeller graph is obtained from an $\infty$-graph by attaching a path to the vertex of degree four, where an $\infty$-graph consists of two cycles with precisely one common vertex. In this paper, we prove that all propeller graphs are determined by their Laplacian spectra as well as their signless Laplacian spectra

The non-bipartite integral graphs with spectral radius three

In this paper, we classify the connected non-bipartite integral graphs with spectral radius three.Comment: 18 pages, 5 figures, 2 table

Spectral integral variation of signed graphs

We characterize when the spectral variation of the signed Laplacian matrices is integral after a new edge is added to a signed graph. As an application, for every fixed signed complete graph, we fully characterize the class of signed graphs to which one can recursively add new edges keeping spectral integral variation to make the signed complete graph.Comment: 18 pages, 0 figur

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM