Abstract: The energy of a graph Γ is the sum of the absolute values of the eigenvalues of the adjacency matrix of Γ. Seidel switching is an operation on the edge set of Γ. In some special cases Seidel switching does not change the spectrum, and therefore the energy. Here we investigate when...

AMS Mathematics Subject Classification: 05C50.

There are eleven integral trees with largest eigenvalue 3.

Given a simple, undirected graph G, Budinich (Discret Appl Math 127:535–543, 2003) proposed a lower bound on the clique number of G by combining the quadratic programming formulation of the clique number due to Motzkin and Straus (Can J Math 17:533–540, 1965) with the spectral decomposition...

Given a simple, undirected graph G, Budinich (Discret Appl Math 127:535–543, 2003) proposed a lower bound on the clique number of G by combining the quadratic programming formulation of the clique number due to Motzkin and Straus (Can J Math 17:533–540, 1965) with the spectral decomposition...

The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited information about the structure of the system....

We analyze growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and hierarchical organization of these graphs, a deterministic...