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Some spectral sufficient conditions for a graph being pancyclic
AIMS Mathematics, 2020 Let $G(V,E)$ be a simple connected graph of order $n$. A graph of order $n$ is called pancyclic if it contains all the cycles $C_k$ for $k\in \{3,4,\cdot\cdot\cdot,n\}$. In this paper, some new spectral sufficient conditions for the graph to be pancyclic
Huan Xu +5 more
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On the α-Spectral Radius of Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2020 For 0 ≤ α ---lt--- 1 and a uniform hypergraph G, the α-spectral radius of G is the largest H-eigenvalue of αD(G)+(1−α)A(G), where D(G) and A(G) are the diagonal tensor of degrees and the adjacency tensor of G, respectively. We give upper bounds for the α-
Guo Haiyan, Zhou Bo
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Some sufficient conditions on hamilton graphs with toughness
Frontiers in Computational Neuroscience, 2022 Let G be a graph, and the number of components of G is denoted by c(G). Let t be a positive real number. A connected graph G is t-tough if tc(G − S) ≤ |S| for every vertex cut S of V(G). The toughness of G is the largest value of t for which G is t-tough,
Gaixiang Cai +4 more
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Maps preserving spectral radius, numerical radius, spectral norm
The Electronic Journal of Linear Algebra, 2007 It was shown by \textit{S. Clark}, \textit{C.K. Li}, and \textit{A. Rastogi} [Bull. Aust. Math. Soc. 77, No.~1, 49--72 (2008; Zbl 1147.15001)] that under some restrictions every (possibly nonlinear) map \(f:M_{m\times n}\to M_{m\times n}\) on rectangular matrices, which is multiplicative with respect to Schur (= entrywise) product, is of the form \(f ...
Li, Chi-Kwong +2 more
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Spectral Radius Formulas Involving Generalized Aluthge Transform
Journal of Function Spaces, 2022 In this paper, we aim to develop formulas of spectral radius for an operator S in terms of generalized Aluthge transform, numerical radius, iterated generalized Aluthge transform, and asymptotic behavior of powers of S.
Zhiqiang Zhang +4 more
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A Sharp upper bound for the spectral radius of a nonnegative matrix and applications [PDF]
, 2016 In this paper, we obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the ...
Shu, Yujie, You, Lihua, Zhang, Xiao-Dong
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Cram\'er transform and t-entropy [PDF]
, 2013 t-entropy is the convex conjugate of the logarithm of the spectral radius of a weighted composition operator (WCO). Let $X$ be a nonnegative random variable.
Ostaszewska, Urszula +1 more
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On the Distance Spectral Radius of Trees with Given Degree Sequence
Discussiones Mathematicae Graph Theory, 2020 We consider the problem of maximizing the distance spectral radius and a slight generalization thereof among all trees with some prescribed degree sequence.
Dadedzi Kenneth +2 more
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Quotient of spectral radius, (signless) Laplacian spectral radius and clique number of graphs [PDF]
Czechoslovak Mathematical Journal, 2016 The author gives sharp lower and upper bounds for the ratio of adjacency spectral radius and the clique number and the ratio of signless Laplacian spectral radius and the clique number, together with characterisation of extremal graphs. These results prove a conjecture from [\textit{M.
Das, Kinkar Ch., Liu, Muhuo
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On the Signless Laplacian Spectral Radius of Graphs without Small Books and Intersecting Quadrangles
Mathematics, 2022 In this paper, we determine the maximum signless Laplacian spectral radius of all graphs which do not contain small books as a subgraph and characterize all extremal graphs. In addition, we give an upper bound of the signless Laplacian spectral radius of
Ming-Zhu Chen +3 more
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