Results 41 to 50 of about 8,535,805 (358)
The approach to criticality in sandpiles [PDF]
, 2010 A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model should be equal
A. A. Járai +8 more
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Algebra and Discrete Mathematics, 2020 In this manuscript, we have evaluated the energies of Smith graphs. In the course of the investigation, we found that only one Smith graph is hypo-energetic. Moreover, we have also established the energy bounds for Smith graphs.
Sharma, P., Naresh, R., Sharma, U.
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Relating graph energy with vertex-degree-based energies
, 2020 Introduction/purpose: The paper presents numerous vertex-degree-based graph invariants considered in the literature. A matrix can be associated to each of these invariants. By means of these matrices, the respective vertex-degree-based graph energies are
I. Gutman
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Descent Steps of a Relation-Aware Energy Produce Heterogeneous Graph Neural Networks [PDF]
Neural Information Processing Systems, 2022 Heterogeneous graph neural networks (GNNs) achieve strong performance on node classification tasks in a semi-supervised learning setting. However, as in the simpler homogeneous GNN case, message-passing-based heterogeneous GNNs may struggle to balance ...
Hongjoon Ahn +4 more
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Belief Propagation on replica symmetric random factor graph models [PDF]
, 2016 According to physics predictions, the free energy of random factor graph models that satisfy a certain "static replica symmetry" condition can be calculated via the Belief Propagation message passing scheme [Krzakala et al., PNAS 2007].
Coja-Oghlan, Amin, Perkins, Will
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Construction of L-equienergetic graphs using some graph operations
AKCE International Journal of Graphs and Combinatorics, 2020 For a graph G with n vertices and m edges, the eigenvalues of its adjacency matrix A(G) are known as eigenvalues of G. The sum of absolute values of eigenvalues of G is called the energy of G.
S. K. Vaidya, Kalpesh M. Popat
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On Energy and Laplacian Energy of Graphs
The Electronic Journal of Linear Algebra, 2016 Let $G=(V,E)$ be a simple graph of order $n$ with $m$ edges. The energy of a graph $G$, denoted by $\mathcal{E}(G)$, is defined as the sum of the absolute values of all eigenvalues of $G$. The Laplacian energy of the graph $G$ is defined as \[ LE = LE(G)=\sum^n_{i=1}\left|\mu_i-\frac{2m}{n}\right| \] where $\mu_1,\,\mu_2,\,\ldots,\,\mu_{n-1 ...
Das, Kinkar Ch., Mojalal, Seyed Ahmad
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Graph states as ground states of many-body spin-1/2 Hamiltonians [PDF]
, 2006 We consider the problem whether graph states can be ground states of local interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at most two-body interactions, we show that no n-qubit graph state can be the exact, non-degenerate ...
H. J. Briegel +4 more
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The total π-electron energy saga: Continuation [PDF]
Kragujevac Journal of ScienceThe total π-electron energy, as calculated within the Hückel molecular orbital approximation, is a much studied quantum chemical characteristics of unsaturated conjugated compounds. Its theory, together with that of its modification called "graph energy",
Gutman Ivan
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Fast evaluation of the adsorption energy of organic molecules on metals via graph neural networks
Nature Computational Science, 2023 Modeling in heterogeneous catalysis requires the extensive evaluation of the energy of molecules adsorbed on surfaces. This is done via density functional theory but for large organic molecules it requires enormous computational time, compromising the ...
Sergio Pablo‐García +6 more
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