Results 1 to 10 of about 175,447 (166)
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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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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On the Spectrum of Threshold Graphs [PDF]
ISRN Discrete Mathematics, 2011 The antiregular connected graph on r vertices is defined as the connected graph whose vertex degrees take the values of r−1 distinct positive integers. We explore the spectrum of its adjacency matrix and show common properties with those of connected threshold graphs, having an equitable partition with a minimal number r of parts.
Sciriha, Irene, Farrugia, Stephanie
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Some Chemistry Indices of Clique-Inserted Graph of a Strongly Regular Graph
Complexity, 2021 In this paper, we give the relation between the spectrum of strongly regular graph and its clique-inserted graph. The Laplacian spectrum and the signless Laplacian spectrum of clique-inserted graph of strongly regular graph are calculated.
Chun-Li Kan +3 more
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Graph Theory: A Lost Component For Development in Nigeria
Journal of Nigerian Society of Physical Sciences, 2022 Graph theory is one of the neglected branches of mathematics in Nigeria but with the most applications in other fields of research. This article shows the paucity, importance, and necessity of graph theory in the development of Nigeria.
Olayiwola Babarinsa
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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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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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On one infinite series of admissible intersection arrays of distance-regular graphs of diameter 5
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. One generalization of one known infinite series of admissible intersection arrays of a bipartite antipodal distance-regular graph is proposed for consideration.
I.T. Mukhamet'yanov
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