Results 211 to 220 of about 4,385,040 (261)

Kirchhoff index of linear pentagonal chains

International Journal of Quantum Chemistry, 2009
AbstractThe resistance distance rij between two vertices vi and vj of a connected 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.
Yan Wang, Wenwen Zhang
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The multiplicative degree-Kirchhoff index and complexity of a class of linear networks

AIMS Mathematics
In this paper, we focus on the strong product of the pentagonal networks. Let $ R_{n} $ be a pentagonal network composed of $ 2n $ pentagons and $ n $ quadrilaterals.
Jia-bao Liu, Kang Wang
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Kirchhoff index of a linear hexagonal chain

2022
Let $H_n$ be a linear hexagonal chain with $n$ hexagons. In this paper, we give a decomposition theorem of Laplacian polynomial of weighted graphs and obtain that the Laplacian spectrum of $H_n$ consists of the eigenvalues of a symmetric tridiagonal matrices of order $4n+2$ and the Laplacian eigenvalues of $2n$ $K_2s$.
Juan Yan, zhenzhen Lou
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Closed-form formulas for Kirchhoff index

International Journal of Quantum Chemistry, 2000
We find closed-form expressions for the resistance, or Kirchhoff index, of certain connected graphs using Foster's theorems, random walks, and the superposition principle. © 2001 John Wiley & Sons, Inc.
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Resistance Distance and Kirchhoff Index of Cayley Graphs on Generalized Quaternion Groups

International Journal of Quantum Chemistry
Based on irreducible representations of generalized quaternion groups, closed‐form formulae of Kirchhoff indices and resistance distances between vertex pairs of Cayley graphs on these groups are given.
Yan Wang, Shuo Zhu, Kai Yuan
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On the Kirchhoff Index of Graphs

Zeitschrift für Naturforschung A, 2013
Let G be a connected graph of order n with Laplacian eigenvalues μ1 ≥ μ2 ≥ ... ≥ μn-1 > mn = 0. The Kirchhoff index of G is defined as [xxx] In this paper. we give lower and upper bounds on Kf of graphs in terms on n, number of edges, maximum degree, and number of spanning trees.
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The weighted Kirchhoff index of a graph

Linear Algebra and its Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mitsuhashi, Hideo, Morita, Hideaki, Sato, Iwao   +2 more
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Extremal polygonal cacti for Wiener index and Kirchhoff index

2020
For a connected graph G, the Wiener index W(G) of G is the sum of the distances of all pairs of vertices, the Kirchhoff index Kf(G) of G is the sum of the resistance distances of all pairs of vertices. A k-polygonal cactus is a connected graph in which the length of every cycle is k and any two cycles have at most one common vertex.
Zeng, Mingyao, Xiao, Qiqi, Tang, Zikai, Deng, Hanyuan   +3 more
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Bounding Robustness via Kirchhoff Index

2017
Bounding robustness in complex networks has gained increasing attention in the literature. Network robustness research has indeed been carried out by scientists with different backgrounds, like mathematics, physics, computer science and biology. As a result, quite a lot of different approaches to capture the robustness properties of a network have been
Monica Bianchi, Gian Paolo Clemente, Alessandra Cornaro, Anna Torriero   +3 more
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Extremal Polygonal Chains with Respectto the Kirchhoff Index

Pure Mathematics
Let G be a simple connected graph. The Kirchhoff index of a graph is the sum of the resistance distance between all vertex pairs in the graph G . The resistance distance in a graph is equivalent to the effective resistance between any node pairs in the ...
成敏 李
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