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The Laplacian spectrum of neural networks [PDF]
Frontiers in Computational Neuroscience, 2014 The brain is a complex network of neural interactions, both at the microscopic and macroscopic level. Graph theory is well suited to examine the global network architecture of these neural networks.
Siemon ede Lange +2 more
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Signless normalized Laplacian for hypergraphs [PDF]
Electronic Journal of Graph Theory and Applications, 2022 The spectral theory of the normalized Laplacian for chemical hypergraphs is further investigated. The signless normalized Laplacian is introduced and it is shown that its spectrum for classical hypergraphs coincides with the spectrum of the normalized ...
Eleonora Andreotti, Raffaella Mulas
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Spektrum Laplace pada graf kincir angin berarah (Q_k^3)
Majalah Ilmiah Matematika dan Statistika, 2022 Suppose that 0 = µ0 ≤ µ1 ≤ ... ≤ µn-1 are eigen values of a Laplacian matrix graph with n vertices and m(µ0), m(µ1), …, m(µn-1) are the multiplicity of each µ, so the Laplacian spectrum of a graph can be expressed as a matrix 2 × n whose line elements ...
Melly Amaliyanah +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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On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$
Karpatsʹkì Matematičnì Publìkacìï, 2021 For a finite commutative ring $\mathbb{Z}_{n}$ with identity $1\neq 0$, the zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $x$ and $y$ are adjacent if and
S. Pirzada, B.A. Rather, T.A. Chishti
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Laplacian energy and first Zagreb index of Laplacian integral graphs
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 The set Si,n = {0, 1, 2, …, i − 1, i + 1, …, n − 1, n}, 1 ⩽ i ⩽ n, is called Laplacian realizable if there exists a simple connected undirected graph whose Laplacian spectrum is Si,n. The existence of such graphs was established by S. Fallat et all.
Hameed Abdul +2 more
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Theory and Applications of Graphs, 2021 In this article, we introduce the concept of nilpotent graph of a finite commutative ring. The set of all non nilpotent elements of a ring is taken as the vertex set and two vertices are adjacent if and only if their sum is nilpotent.
Dhiren Basnet, Ajay Sharma, Rahul Dutta
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Hyper-Wiener index and Laplacian spectrum [PDF]
Journal of the Serbian Chemical Society, 2003 The hyper-Wiener index WWW of a chemical tree T is defined as the sum of the product n1 n2 n3, over all pairs u, u of vertices of T, where n1 and n2 are the number of vertices of T, lying on the two sides of the path which connects u and u, and n3 is the
IVAN GUTMAN
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Distance (signless) Laplacian spectrum of dumbbell graphs [PDF]
Transactions on Combinatorics, 2023 In this paper, we determine the distance Laplacian and distance signless Laplacian spectrum of generalized wheel graphs and a new class of graphs called dumbbell graphs.
Sakthidevi Kaliyaperumal +1 more
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Results on Laplacian spectra of graphs with pockets
AKCE International Journal of Graphs and Combinatorics, 2018 Let F , H v be simple connected graphs on n and m + 1 vertices, respectively. Let v be a specified vertex of H v and u 1 , … , u k ∈ F . Then the graph G = G [ F , u 1 , … , u k , H v ] obtained by taking one copy of F and k copies of H v , and then ...
Sasmita Barik, Gopinath Sahoo
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