Results 51 to 60 of about 2,691 (126)
A unified perspective on some autocorrelation measures in different fields: A note
Open Mathematics, 2023 Using notions from linear algebraic graph theory, this article provides a unified perspective on some autocorrelation measures in different fields. They are as follows: (a) Orcutt’s first serial correlation coefficient, (b) Anderson’s first circular ...
Yamada Hiroshi
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On inverse sum indeg energy of graphs
Special Matrices, 2023 For a simple graph with vertex set {v1,v2,…,vn}\left\{{v}_{1},{v}_{2},\ldots ,{v}_{n}\right\} and degree sequence dvii=1,2,…,n{d}_{{v}_{i}}\hspace{0.33em}i=1,2,\ldots ,n, the inverse sum indeg matrix (ISI matrix) AISI(G)=(aij){A}_{{\rm{ISI}}}\left(G ...
Jamal Fareeha +2 more
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Retraction Note: On the Kirchhoff matrix, a new Kirchhoff index and the Kirchhoff energy
, 2014 The main purpose of this paper is to define and investigate the Kirchhoff matrix, a new Kirchhoff index, the Kirchhoff energy and the Kirchhoff Estrada index of a graph.
A. D. Maden +3 more
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On the distance energy of k-uniform hypergraphs
Special Matrices, 2023 In this article, we extend the concept of distance energy for hypergraphs. We first establish a relation between the distance energy and the distance spectral radius.
Sharma Kshitij, Panda Swarup Kumar
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More Tales of Hoffman: Bounds for the Vector Chromatic Number of a Graph
Discussiones Mathematicae Graph Theory, 2023 Let χ(G) denote the chromatic number of a graph and χv(G) denote the vector chromatic number. For all graphs χv(G) ≤ χ(G) and for some graphs χv(G) ≪ χ(G).
Wocjan Pawel +2 more
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Max k-cut and the smallest eigenvalue
, 2016 Let $G$ be a graph of order $n$ and size $m$, and let $\mathrm{mc}_{k}\left( G\right) $ be the maximum size of a $k$-cut of $G.$ It is shown that \[ \mathrm{mc}_{k}\left( G\right) \leq\frac{k-1}{k}\left( m-\frac{\mu_{\min }\left( G\right) n}{2}\right) , \
Nikiforov, V.
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Existence and uniqueness of solutions to the norm minimum problem on digraphs
Open Mathematics, 2022 In this article, based on the path homology theory of digraphs, which has been initiated and studied by Grigor’yan, Lin, Muranov, and Yau, we prove the existence and uniqueness of solutions to the problem ∥w∥=minu∈Ω2(G),u≠012∥∂u−w∥22+∣u∣1\parallel w ...
Wang Chong
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The Algebraic Connectivity of a Graph and its Complement
, 2018 For a graph $G$, let $\lambda_2(G)$ denote its second smallest Laplacian eigenvalue. It was conjectured that $\lambda_2(G) + \lambda_2(\overline G) \ge 1$, where $\overline G$ is the complement of $G$. In this paper, it is shown that $\max\{\lambda_2(G),
Afshari, B. +3 more
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The Aα-spectral radius of complements of bicyclic and tricyclic graphs with n vertices
Special Matrices, 2021 Recently, the extremal problem of the spectral radius in the class of complements of trees, unicyclic graphs, bicyclic graphs and tricyclic graphs had been studied widely.
Chen Chaohui +2 more
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A short note on a short remark of Graham and Lov\'{a}sz [PDF]
, 2013 Let D be the distance matrix of a connected graph G and let nn(G), np(G) be the number of strictly negative and positive eigenvalues of D respectively. It was remarked in [1] that it is not known whether there is a graph for which np(G) > nn (G). In this
Azarija, Jernej
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