A p-rose graph = RG(a3; a4; : : : ; as) is a graph consisting of p = a3 + a4 + + as 2 cycles that all meet in one vertex, and ai (3 i s) is the number of cycles in of length 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 (2018) 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.
SIGNLESS LAPLACIAN SPECTRAL CHARACTERIZATION OF ROSES / Brunetti, M; Ashrafi, A R; Abdian, A Z. - In: MAGALLAT AL-KUWAYT LI-L-ʿULUM. - ISSN 2307-4108. - 47:4(2020), pp. 12-18.
SIGNLESS LAPLACIAN SPECTRAL CHARACTERIZATION OF ROSES
Brunetti M;
2020
Abstract
A p-rose graph = RG(a3; a4; : : : ; as) is a graph consisting of p = a3 + a4 + + as 2 cycles that all meet in one vertex, and ai (3 i s) is the number of cycles in of length 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 (2018) 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.| File | Dimensione | Formato | |
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