Solutions for two conjectures on the eigenvalues of the eccentricity matrix, and beyond

Wei, Wei; He, Xiaocong; Li, Shuchao

doi:10.1016/j.disc.2020.111925

Cited by 32 publications

(8 citation statements)

References 7 publications

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“…The weights of different evaluation indexes are obtained according to the eigenvalues of the comparison matrix [23,24], and the construction of the flipped classroom teaching quality evaluation system in colleges and universities is completed.…”

Section: Constructing the Quality Evaluation System Of Flippedmentioning

confidence: 99%

Teaching Quality Evaluation Model of a Flipped Classroom in Colleges and Universities Based on Support Vector Machine

Li²

2022

Wireless Communications and Mobile Computing

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The systematic evaluation of teaching quality in colleges and universities is an important factor, which makes the systematic evaluation of teaching quality in colleges and universities very complex and makes the systematic evaluation of teaching quality in colleges and universities unable to describe a variety of teaching quality directly or indirectly. Therefore, a quality evaluation model of flipped classroom teaching in colleges and universities based on support vector machine is proposed. Through the selection of teaching quality evaluation indicators from three aspects of experts, teachers, and students, the evaluation system of flipped classroom teaching quality in colleges and universities is established. The evaluation indicators are used as the input of support vector machine for learning, and the evaluation model of flipped classroom teaching quality in colleges and universities is established. The experimental results show that this method can effectively evaluate the quality of flipped classroom teaching in colleges and universities, the relative error of the evaluation results is low, and it has certain practicability.

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Section: Constructing the Quality Evaluation System Of Flippedmentioning

confidence: 99%

Teaching Quality Evaluation Model of a Flipped Classroom in Colleges and Universities Based on Support Vector Machine

Li²

2022

Wireless Communications and Mobile Computing

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“…Wang et al [17] showed that the eccentricity matrix of trees is irreducible and investigated the relations between the eigenvalues of the adjacency and eccentricity matrices. Wei, He and Li [20] determined the trees with given diameter or fixed order minimizing the ǫspectral radius. Wang et al [18] and Mahato et al [11] respectively determined the lower and upper bounds for the ǫ-spectral radius of graphs, and identified the corresponding extremal graphs.…”

Section: Introductionmentioning

confidence: 99%

The ϵ-spectral radii of k-uniform hypertrees *

Liu

2023

Preprint

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The \epsilon-spectral radius of a connected hypergraph is the largest eigenvalue of its eccentricity matrix. Let \mathcal{T}_{m,d} be the set of k-uniform hypertrees with size m and diameter d. In this paper, we show that the eccentricity matrix of a k-uniform hypertree is irreducible, and we characterize the unique hypertrees with the minimum-spectral radius among \bigcup_{d\neq3}\mathcal{T}_{m,d}. AMS Classi cation: 05C50, 05C65

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“…Mahato et al [6] studied the spectra of eccentricity matrices of graphs. Recently, Wei et al [16] characterized the trees which have the minimum E-spectral radius with the given diameter. As a consequence, they determined the trees on n vertices with minimum E-spectral radius, which solved a conjecture posted in [14].…”

Section: Introductionmentioning

confidence: 99%

On the eccentricity matrices of trees: Inertia and spectral symmetry

Mahato¹,

Kannan²

2022

Preprint

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The eccentricity matrix E(G) of a connected graph G is obtained from the distance matrix of G by keeping the largest non-zero entries in each row and each column, and leaving zeros in the remaining ones. The eigenvalues of E(G) are the E-eigenvalues of G. In this article, we find the inertia of the eccentricity matrices of trees. Interestingly, any tree on more than 4 vertices with odd diameter has two positive and two negative E-eigenvalues (irrespective of the structure of the tree). A tree with even diameter has the same number of positive and negative E-eigenvalues, which is equal to the number of 'diametrically distinguished' vertices (see Definition 3.1). Besides we prove that the spectrum of the eccentricity matrix of a tree is symmetric with respect to the origin if and only if the tree has odd diameter. As an application, we characterize the trees with three distinct E-eigenvalues.

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Solutions for two conjectures on the eigenvalues of the eccentricity matrix, and beyond

Cited by 32 publications

References 7 publications

Teaching Quality Evaluation Model of a Flipped Classroom in Colleges and Universities Based on Support Vector Machine

Teaching Quality Evaluation Model of a Flipped Classroom in Colleges and Universities Based on Support Vector Machine

The ϵ-spectral radii of k-uniform hypertrees *

On the eccentricity matrices of trees: Inertia and spectral symmetry

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