19.
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.
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