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On the Kirchhoff index of a graph and the matchings of the subdivision
Discrete Applied Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Linfeng Que, Haiyan Chen
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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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Chemical Physics Letters, 2008
We report lower bounds for the Kirchhoff index of a connected ( molecular) graph in terms of its structural parameters such as the number of vertices ( atoms), the number of edges ( bonds), maximum vertex degree ( valency), connectivity and chromatic number.
Zhou Bo, Trinajstić, Nenad
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We report lower bounds for the Kirchhoff index of a connected ( molecular) graph in terms of its structural parameters such as the number of vertices ( atoms), the number of edges ( bonds), maximum vertex degree ( valency), connectivity and chromatic number.
Zhou Bo, Trinajstić, Nenad
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Kirchhoff index of simplicial networks
Linear Algebra and its Applications, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kook, Woong, Lee, Kang-Ju
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On the Kirchhoff Index of Graphs
Zeitschrift für Naturforschung A, 2013Let 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, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mitsuhashi, Hideo +2 more
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Simplicial Kirchhoff index of random complexes
Advances in Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Woong Kook, Kang-Ju Lee
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On the Kirchhoff index of regular graphs
International Journal of Quantum Chemistry, 2009AbstractUsing probabilistic tools, we give a compact formula for the Kirchhoff index of any d‐regular N‐vertex graph in terms of d, N, and Kemeny's constant, as well as general upper and lower bounds in terms of d and N. © 2009 Wiley Periodicals, Inc.
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Extremal polyphenyl chains with respect to the Kirchhoff index
Theoretical Computer ScienceThe Kirchhoff index of a graph is the sum of the resistance distance between all vertex pairs in the graph \(G\). A graph with \(n\) hexagons where each hexagon is reduced to a vertex and can connect to a path is called a polyphenyl chain. The authors in this paper characterize the polyphenyl chains with maximal and minimal Kirchhoff index.
Chengmin Li, Hong Bian, Haizheng Yu
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Resistance Distance and Kirchhoff Index in Windmill Graphs
Current Organic SynthesisIntroduction: The objective of this study is to compute the Kirchhoff index and re-sistance distance for two classes of windmill graphs, namely the French windmill graph and the Dutch windmill graph. Methods: In this study, G is considered a simple connected graph with vertex set V (G) and edge set E(G).
Muhammad Shoaib, Sardar, Shou-Jun, Xu
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