On the Eigenvalues of some Class of Pseudo-linear Transformations
Cover matrices of posets and their spectra
We analyze the spectra of the cover matrix of a given poset. Some consequences on the multiplicities are provided.
Relations between -regular sets and star complements
Let be a finite graph with an eigenvalue of multiplicity . A set of vertices in is called a star set for in if is not an eigenvalue of the star complement which is the subgraph of induced by vertices not in . A vertex subset of a graph is -regular if it induces a -regular subgraph and every vertex not in the subset has neighbors in it. We investigate the graphs having a -regular set which induces a star complement for some eigenvalue. A survey of known results is provided...
Tridiagonal matrices and spectral properties of some graph classes
A graph is called a chain graph if it is bipartite and the neighbourhoods of the vertices in each colour class form a chain with respect to inclusion. In this paper we give an explicit formula for the characteristic polynomial of any chain graph and we show that it can be expressed using the determinant of a particular tridiagonal matrix. Then this fact is applied to show that in a certain interval a chain graph does not have any nonzero eigenvalue. A similar result is provided for threshold graphs....
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