Signless Laplacian spectral characterization of roses

Abstract EN

A p-rose graph I RG(a3, a4,....a,) is a graph consisting of p = a3 + a4 + +as > 2 cycles that all meet in one vertex, and a; (3 < i

A graph G is said to be DLS (resp.

DQS) if it is determined by the spectrum of its Laplacian (resp.

signless Laplacian) matrix, i.e., if every graph with the same spectrum is isomorphic to G.

He and van Dam recently proved that all p-roses, except for two non-isomorphic exceptions, are DLS.

In this paper, we show that, for p > 3 all p-roses are DQS.