Bounds for the (Laplacian) spectral radius of graphs with parameter α

Tian, Gui-Xian; Huang, Ting‐Zhu

doi:10.1007/s10587-012-0030-9

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Satisfies the Following Conditions2

Bounds For Spectral Radius Of Various Matrices Associated Wi...1

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Cited by 2 publications

(3 citation statements)

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“…≥ d n be degree sequence of G. Denote by m i the average degree of a vertex v i , which is j∼i dj di . In [11,15], authors introduced the following notation: for any real number α,…”

Section: Bounds For Spectral Radius Of Various Matrices Associated Wi...mentioning

confidence: 99%

“…where ∆ is the maximum degree of G, N = max i∼j {d j /d i }. Moreover, the equality holds in (15) if and only if…”

Section: Satisfies the Following Conditionsmentioning

confidence: 99%

“…Remark that the equality holds in (15) for some 2 ≤ i ≤ n whenever G is a bidegreed graph in which . Now we introduce the following notation: for any real number α,…”

Section: Satisfies the Following Conditionsmentioning

confidence: 99%

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Bounds on the spectral radius of nonnegative matrices and applications in graph spectra

Cui,

Tian

2013

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In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B. Zhou, Sharp bounds on the spectral radius of a nonnegative matrix, Linear Algebra Appl. ( 2013), http://dx.doi.org/10.1016/j.laa.2013.08.026]. Finally, applying these bounds to various matrices associated with a graph, we obtain some new upper and lower bounds on various spectral radiuses of graphs, which generalize and improve some known results.

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“…≥ d n be degree sequence of G. Denote by m i the average degree of a vertex v i , which is j∼i dj di . In [11,15], authors introduced the following notation: for any real number α,…”

Section: Bounds For Spectral Radius Of Various Matrices Associated Wi...mentioning

confidence: 99%

“…where ∆ is the maximum degree of G, N = max i∼j {d j /d i }. Moreover, the equality holds in (15) if and only if…”

Section: Satisfies the Following Conditionsmentioning

confidence: 99%