Results 11 to 20 of about 287 (207)
Spectral characterizations of sun graphs and broken sun graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Several matrices can be associated to a graph such as the adjacency matrix or the Laplacian matrix. The spectrum of these matrices gives some informations about the structure of the graph and the question ''Which graphs are determined by their spectrum?''
Romain Boulet
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The distance spectrum of two new operations of graphs [PDF]
Transactions on Combinatorics, 2020 Let $G$ be a connected graph with vertex set $V(G)=\{v_1, v_2,\ldots,v_n\}$. The distance matrix $D=D(G)$ of $G$ is defined so that its $(i,j)$-entry is equal to the distance $d_G(v_i,v_j)$ between the vertices $v_i$ and $v_j$ of $G$. The eigenvalues
Zikai Tang +3 more
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Geometry-Aware Cell Detection with Deep Learning
mSystems, 2020 Analyzing cells and tissues under a microscope is a cornerstone of biological research and clinical practice. However, the challenge faced by conventional microscopy image analysis is the fact that cell recognition through a microscope is still time ...
Hao Jiang +5 more
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The non-negative spectrum of a digraph
Open Mathematics, 2020 Given the adjacency matrix A of a digraph, the eigenvalues of the matrix AAT constitute the so-called non-negative spectrum of this digraph. We investigate the relation between the structure of digraphs and their non-negative spectra and associated ...
Alomari Omar +2 more
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Cospectral constructions for several graph matrices using cousin vertices
Special Matrices, 2021 Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum.
Lorenzen Kate
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Computing the Energy and Estrada Index of Different Molecular Structures
Journal of Chemistry, 2022 Graph energy is an invariant that is derived from the spectrum of the adjacency matrix of a graph. Graph energy is actually the absolute sum of all the eigenvalues of the adjacency matrix of a graph i.e.
Zeeshan Saleem Mufti +5 more
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The spectral determination of the connected multicone graphs
AKCE International Journal of Graphs and Combinatorics, 2021 The main goal of the paper is to answer an unsolved problem. A multicone graph is defined to be the join of a clique and a regular graph, and a wheel as the join of a vertex and a cycle.
Ali Zeydi Abdian +4 more
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A new matrix representation of multidigraphs
AKCE International Journal of Graphs and Combinatorics, 2020 In this article, we introduce a new matrix associated with a multidigraph, named as the complex adjacency matrix. We study the spectral properties of bipartite multidigraphs corresponding to the complex adjacency matrix.
Sasmita Barik, Gopinath Sahoo
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On the Displacement of Eigenvalues When Removing a Twin Vertex
Discussiones Mathematicae Graph Theory, 2020 Twin vertices of a graph have the same open neighbourhood. If they are not adjacent, then they are called duplicates and contribute the eigenvalue zero to the adjacency matrix.
Briffa Johann A., Sciriha Irene
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On the Maximal-Adjacency-Spectrum Unicyclic Graphs with Given Maximum Degree
Mathematical Problems in Engineering, 2020 In this paper, we study the properties and structure of the maximal-adjacency-spectrum unicyclic graphs with given maximum degree. We obtain some necessary conditions on the maximal-adjacency-spectrum unicyclic graphs in the set of unicyclic graphs with n vertices and maximum degree Δ and describe the structure of the maximal-adjacency-spectrum ...
Haizhou Song, Lulu Tian
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