On a signless Laplacian spectral characterization of [formula omitted]-shape trees

Abstract

Let M be an associated matrix of a graph G (the adjacency, Laplacian and signless Laplacian matrix). Two graphs are said to be cospectral with respect to M if they have the same M spectrum. A graph is said to be determined by M spectrum if there is no other non-isomorphic graph with the same spectrum with respect to M . It is shown that T -shape trees are determined by their Laplacian spectra. Moreover among them those are determined by their adjacency spectra are characterized. In this paper, we identify graphs which are cospectral to a given T -shape tree with respect to the signless Laplacian matrix. Subsequently, T -shape trees which are determined by their signless Laplacian spectra are identified.