arXiv subjects

M. Mitjana

Publications and source records attributed to M. Mitjana.

3 recordsLinked to original sources

arXiv2016

On middle cube graphs

We study a family of graphs related to the $n$-cube. The middle cube graph of parameter $k$ is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors).

math.CO↗

arXiv2015

The inverse matrix of some circulant matrices

We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the solution of boundary value problems associated to second order linear difffference equations. Consequently, we reduce the computational cost of the problem. In particular, we recover the inverses of some well known circulant matrices whose coeffifficients are arithmetic or geometric sequences, Horadam numbers among others. We also characterize when a general symmetric circulant and tridiagonal matrix is invertible and in this case, we compute explicitly its inverse.

math.CA↗

arXiv2015

Green Operators of Networks with a new vertex

Any elliptic operator defines an automorphism on the orthogonal subspace to the eigenfunctions associated with the lowest eigenvalue, whose inverse is the orthogonal Green operator. In this study, we show that elliptic Schrödinger operators on networks that have been obtained by adding a new vertex to a given network, can be seen as perturbations of the Schrödinger operators on the initial network. Therefore, the Green function on the new network can be computed in terms of the Green function of the original network.

math.SP↗