Results 1 to 10 of about 6,673 (197)
Some New Bounds for α-Adjacency Energy of Graphs
Mathematics, 2023 Let G be a graph with the adjacency matrix A(G), and let D(G) be the diagonal matrix of the degrees of G. Nikiforov first defined the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), 0≤α≤1, which shed new light on A(G) and Q(G)=D(G)+A(G), and yielded some ...
Haixia Zhang, Zhuolin Zhang
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The gamma-Signless Laplacian Adjacency Matrix of Mixed Graphs
Theory and Applications of Graphs, 2023 The α-Hermitian adjacency matrix Hα of a mixed graph X has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number α.
Omar Alomari +2 more
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A Note on the Estrada Index of the Aα-Matrix
Mathematics, 2021 Let G be a graph on n vertices. The Estrada index of G is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. V. Nikiforov studied hybrids of A(G) and D(G) and defined the Aα-matrix for every real α∈[0,1] as: Aα(G)=αD(
Jonnathan Rodríguez, Hans Nina
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On α-adjacency energy of graphs and Zagreb index
AKCE International Journal of Graphs and Combinatorics, 2021 Let A(G) be the adjacency matrix and D(G) be the diagonal matrix of the vertex degrees of a simple connected graph G. Nikiforov defined the matrix of the convex combinations of D(G) and A(G) as for If are the eigenvalues of (which we call α-adjacency ...
S. Pirzada +3 more
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$ A_{\alpha} $ matrix of commuting graphs of non-abelian groups
AIMS Mathematics, 2022 For a finite group $ \mathcal{G} $ and a subset $ X\neq \emptyset $ of $ \mathcal{G} $, the commuting graph, indicated by $ G = \mathcal{C}(\mathcal{G}, X) $, is the simple connected graph with vertex set $ X $ and two distinct vertices $ x $ and $ y $
Bilal A. Rather +5 more
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On the Generalized Adjacency Spread of a Graph
Mathematics, 2023 For a simple finite graph G, the generalized adjacency matrix is defined as Aα(G)=αD(G)+(1−α)A(G),α∈[0,1], where A(G) and D(G) are respectively the adjacency matrix and diagonal matrix of the vertex degrees.
Maryam Baghipur +3 more
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Combinatorics of Nahm sums, quiver resultants and the K-theoretic condition
Journal of High Energy Physics, 2021 Algebraic Nahm equations, considered in the paper, are polynomial equations, governing the q → 1 limit of the q-hypergeometric Nahm sums. They make an appearance in various fields: hyperbolic geometry, knot theory, quiver representation theory ...
Dmitry Noshchenko
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Wiener index and addressing of some finite graphs
AKCE International Journal of Graphs and Combinatorics, 2023 An addressing of length t of a graph G is an assignment of t-tuples with entries in [Formula: see text] called addresses, to the vertices of G such that the distance between any two vertices can be determined from their addresses.
Mona Gholamnia Taleshani, Ahmad Abbasi
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A Note on Some Bounds of the α-Estrada Index of Graphs
Advances in Mathematical Physics, 2020 Let G be a simple graph with n vertices. Let A~αG=αDG+1−αAG, where 0≤α≤1 and AG and DG denote the adjacency matrix and degree matrix of G, respectively. EEαG=∑i=1neλi is called the α-Estrada index of G, where λ1,⋯,λn denote the eigenvalues of A~αG.
Yang Yang, Lizhu Sun, Changjiang Bu
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New Bounds for the α-Indices of Graphs
Mathematics, 2020 Let G be a graph, for any real 0≤α≤1, Nikiforov defines the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and diagonal matrix of degrees of the vertices of G.
Eber Lenes +2 more
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