Authors: | Belardo, Francesco Li Marzi, Enzo Simić, Slobodan Wang, Jianfeng |

Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts |

Title: | Graphs whose signless Laplacian spectral radius does not exceed the Hoffman limit value |

Journal: | Linear Algebra and Its Applications |

Volume: | 435 |

Issue: | 11 |

First page: | 2913 |

Last page: | 2920 |

Issue Date: | 1-Dec-2011 |

Rank: | M22 |

ISSN: | 0024-3795 |

DOI: | 10.1016/j.laa.2011.05.006 |

Abstract: | For a graph matrix M, the Hoffman limit value H(M) is the limit (if it exists) of the largest eigenvalue (or, M-index, for short) of M(Hn), where the graph Hn is obtained by attaching a pendant edge to the cycle Cn-1 of length n-1. In spectral graph theory, M is usually either the adjacency matrix A or the Laplacian matrix L or the signless Laplacian matrix Q. The exact values of H(A) and H(L) were first determined by Hoffman and Guo, respectively. Since Hn is bipartite for odd n, we have H(Q)=H(L). All graphs whose A-index is not greater than H(A) were completely described in the literature. In the present paper, we determine all graphs whose Q-index does not exceed H(Q). The results obtained are determinant to describe all graphs whose L-index is not greater then H(L). This is done precisely in Wang et al. (in press) [21]. |

Keywords: | Hoffman limit value | Index | Limit point of the eigenvalues | Signless Laplacian matrix | Spectral radius |

Publisher: | Elsevier |

Project: | PRIN 2008 (Italy) “Disegni Combinatorici, Grafi e loro Applicazioni” Serbian Ministry of Science, Grant no. 144015 Graph theory and mathematical programming with applications in chemistry and computer science National Science Foundation of China (No. 10961023) NSFQH (SRIPQHNU) (No. 2011-ZR-616) |

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