Results 1 to 10 of about 150,128 (137)
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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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 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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Hermitian adjacency matrix of the second kind for mixed graphs [PDF]
Discrete Mathematics, 2021 This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind introduced by Mohar [21]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u ...
Shuchao Li, Yuantian Yu
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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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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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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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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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On the adjacency matrix of a complex unit gain graph [PDF]
Linear and multilinear algebra, 2018 A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge.
Ranjit Mehatari +2 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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