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Kirchhoff index of Vicsek polygon networks and its applications
Chaos, Solitons and FractalsZhiqiang Wu +4 more
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Simplicial Kirchhoff index of random complexes
Advances in Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
W. Kook, Kang-Ju Lee
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The Kirchhoff index and the matching number
International Journal of Quantum Chemistry, 2008AbstractThe Kirchhoff index of a connected (molecular) graph is the sum of the resistance‐distances between all unordered pairs of vertices and may also be expressed by its Laplacian eigenvalues. We determine the minimum Kirchhoff index of connected (molecular) graphs in terms of the number of vertices and matching number and characterize the unique ...
Zhou, Bo, Trinajstic, Nenad
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Extremal linear triangular chains with respect to the Kirchhoff index
Zeitschrift für Naturforschung ALet G be a connected graph. The resistance distance among two vertices is defined as the effective resistance between the corresponding nodes in the electrical network constructed from G by replacing each edge with a unit resistor. The Kirchhoff index is
Wensheng Sun, Yujun Yang, Shoujun Xu
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International Journal of Quantum Chemistry, 2018
AbstractLet Hn be a linear crossed hexagonal chain with n crossed hexagonals. In this article, we find that the Laplacian (resp. normalized Laplacian) spectrum of Hn consists of the eigenvalues of a symmetric tridiagonal matrix of order 2n + 1 and a diagonal matrix of order 2n + 1.
Yingui Pan, Jianping Li
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AbstractLet Hn be a linear crossed hexagonal chain with n crossed hexagonals. In this article, we find that the Laplacian (resp. normalized Laplacian) spectrum of Hn consists of the eigenvalues of a symmetric tridiagonal matrix of order 2n + 1 and a diagonal matrix of order 2n + 1.
Yingui Pan, Jianping Li
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Degree Kirchhoff Index of Bicyclic Graphs
Canadian Mathematical Bulletin, 2017AbstractLet G be a connected graph with vertex set V(G).The degree Kirchhoò index of G is defined as S'(G) = Σ{u,v}⊆V(G) d(u)d(v)R(u, v), where d(u) is the degree of vertex u, and R(u, v) denotes the resistance distance between vertices u and v. In this paper, we characterize the graphs having maximum and minimum degree Kirchhoò index among all n ...
Zikai Tang, Hanyuan Deng
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On the Kirchhoff index for circulant graph with non-fixed jumps
Mathematical Structures and ModelingThis article deals with a graph invariant called the Kirchhoff index. An explicit analytical formula for the Kirchhoff index of circulant graphs with non-fixed jumps is defined.
G. Sokolova
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Kirchhoff Index for Circulant Graphs and Its Asymptotics
Doklady Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mednykh, A. D., Mednykh, I. A.
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Kirchhoff index of linear hexagonal chains
International Journal of Quantum Chemistry, 2007AbstractThe resistance distance rij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices.
Yujun Yang, Heping Zhang
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Resistance distance and Kirchhoff index of two kinds of double join operations on graphs
Discrete Mathematics and ApplicationsLet G be a connected graph. The resistance distance between any two vertices of G is defined to be the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index of G is the sum of resistance distances
Weizhong Wang, Tingyan Ma
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