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Spectrum knowledge graph: an intelligent engine facing future spectrum management [PDF]
Tongxin xuebao, 2021 To solve the issues of simple representations on spectrum situation, much dependence on artificial experience in manual management and low efficiency and accuracy in the current spectrum management, meeting the requirements of automation, precision and ...
Jiachen SUN +4 more
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Approximating the Spectrum of a Graph [PDF]
Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2018 The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph, including the extent to which the graph posses community structures at multiple scales.
Cohen-Steiner, David +3 more
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The Spectrum of Triangle-Free Graphs
SIAM Journal on Discrete Mathematics, 2023 Denote by $q_n(G)$ the smallest eigenvalue of the signless Laplacian matrix of an $n$-vertex graph $G$. Brandt conjectured in 1997 that for regular triangle-free graphs $q_n(G) \leq \frac{4n}{25}$. We prove a stronger result: If $G$ is a triangle-free graph then $q_n(G) \leq \frac{15n}{94}< \frac{4n}{25}$.
József Balogh +4 more
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Determining Graphs by the Complementary Spectrum
Discussiones Mathematicae Graph Theory, 2020 The complementary spectrum of a connected graph G is the set of the complementary eigenvalues of the adjacency matrix of G. In this note, we discuss the possibility of representing G using this spectrum.
Pinheiro Lucélia K. +2 more
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Bounds on spectrum graph coloring [PDF]
Electronic Notes in Discrete Mathematics, 2016 Ministerio de Economía y ...
Orden Martín, David +3 more
core +4 more sources
On the Spectrum of a Complete Multipartite Graph
European Journal of Combinatorics, 1980 The spectrum S(G) of a graph G is defined as the sequence of eigenvalues of its adjacency matrix. The spectrum of a complete multipartite graph K has several remarkable properties. John Smith has shown that a graph has exactly one positive eigenvalue if and only if the non-isolated points form a complete multipartite graph.
Friedrich Esser, Frank Harary
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Spectrum‐sensing algorithm based on graph feature fusion
IET Radar, Sonar & NavigationGraph‐based spectrum sensing in noisy environments has major implications for civilian and military signal processing applications. However, existing algorithms suffer from high computational complexity and performance deterioration at low signal‐to ...
Shanshan Wu, Guobing Hu, Bin Gu
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Relating Estrada index with spectral radius [PDF]
Journal of the Serbian Chemical Society, 2007 The Estrada index EE is a recently proposed molecular structure-descriptor, used in the modeling of certain features of the 3D structure of organic molecules, in particular of the degree of folding of proteins and other long-chain biopolymers.
Gutman Ivan +4 more
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Maximum Entropy Approach to Massive Graph Spectrum Learning with Applications
Algorithms, 2022 We propose an alternative maximum entropy approach to learning the spectra of massive graphs. In contrast to state-of-the-art Lanczos algorithm for spectral density estimation and applications thereof, our approach does not require kernel smoothing.
Diego Granziol +5 more
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Spectrum of the Transposition graph
Linear Algebra and its Applications, 2022 Transposition graph $T_n$ is defined as a Cayley graph over the symmetric group generated by all transpositions. It is known that all eigenvalues of $T_n$ are integers. However, an explicit description of the spectrum is unknown. In this paper we prove that for any integer $k\geqslant 0$ there exists $n_0$ such that for any $n\geqslant n_0$ and any $m \
Elena V. Konstantinova, Artem Kravchuk
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