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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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On α-adjacency energy of graphs and Zagreb index [PDF]
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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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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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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Centerless Multi-View K-means Based on the Adjacency Matrix
AAAI Conference on Artificial Intelligence, 2023 Although K-Means clustering has been widely studied due to its simplicity, these methods still have the following fatal drawbacks. Firstly, they need to initialize the cluster centers, which causes unstable clustering performance.
Han Lu +4 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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Graceful labeling construction for some special tree graph using adjacency matrix
Electronic Journal of Graph Theory and Applications, 2023 In 1967, Rosa introduced β − labeling which was then popularized by Golomb under the name graceful. Graceful labeling on a graph G is an injective function f : V ( G ) → { 0 , 1 , 2 , . . .
Nikson Simarmata +2 more
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Extremal Problems for Graphical Function-Indices and f-Weighted Adjacency Matrix
Discrete Mathematics Letters, 2022 Let f(x, y) (f(x)) be a symmetric real function (real function) and G = (V,E) be a graph. Denote by di the degree of a vertex i in G. The graphical function-index TIf (G) (Hf (G)) of G with edge-weight (vertex-weight) function f(x, y) (f(x)) is defined ...
Xueliang Li, Danni Peng
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General Zagreb Adjacency Matrix
Contributions to Mathematics, 2022 Let A ( G ) and D ( G ) be the adjacency matrix and the degree diagonal matrix of a graph G , respectively. For any real number α , the general Zagreb adjacency matrix of G is defined as Z α ( G ) = D α ( G )+ A ( G ) .
Zhen Lin
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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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