Results 21 to 30 of about 3,634,246 (271)
Kirchhoff index of a non-complete wheel [PDF]
Electronic Notes in Discrete Mathematics, 2016 In this work, we compute analitycally the Kirchhoff index and effective resistances of a weighted non–complete wheel that has been obtained by adding a vertex to a weighted cycle and some edges conveniently chosen.
Gago Álvarez, Silvia
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Note on degree Kirchhoff index of graphs [PDF]
Transactions on Combinatorics, 2013 Bounds for the degree Kirchhoff index of the line and para-line graphs are determined.The special case of regular graphs is analyzed in due detail.
Mardjan Hakimi-Nezhaad +2 more
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Extremal Kirchhoff index in polycyclic chains
Discrete Applied MathematicsThe Kirchhoff index of graphs, introduced by Klein and Randić in 1993, has been known useful in the study of computer science, complex network and quantum chemistry. The Kirchhoff index of a graph $G$ is defined as $Kf(G)=\sum\limits_{\{u,v\}\subseteq V(G)}Ω_{G}(u,v)$, where $Ω_{G}(u,v)$ denotes the resistance distance between $u$ and $v$ in $G$.
Lihua You, Hechao Liu
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On Laplacian resolvent energy of graphs [PDF]
Transactions on Combinatorics, 2023 Let $G$ be a simple connected graph of order $n$ and size $m$. The matrix $L(G)=D(G)-A(G)$ is the Laplacian matrix of $G$, where $D(G)$ and $A(G)$ are the degree diagonal matrix and the adjacency matrix, respectively. For the graph $G$, let $d_{1}\geq d_{
Sandeep Bhatnagar +2 more
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Comparison of the Wiener and Kirchhoff Indices of Random Pentachains
Journal of Mathematics, 2021 Let G be a connected (molecule) graph. The Wiener index WG and Kirchhoff index KfG of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G, respectively.
Shouliu Wei +3 more
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On relation between the Kirchhoff index and number of spanning trees of graph [PDF]
Communications in Combinatorics and Optimization, 2020 Let $G$ be a simple connected graph with degree sequence $(d_1,d_2,\ldots, d_n)$ where $\Delta =d_1\geq d_2\geq\cdots\geq d_n=\delta >0$ and let $\mu_1\geq \mu_2\geq\cdots\geq\mu_{n-1}>\mu_n=0$ be the Laplacian eigenvalues of $G$.
Igor Milovanovic +3 more
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Retraction Note: On the Kirchhoff matrix, a new Kirchhoff index and the Kirchhoff energy [PDF]
Journal of Inequalities and Applications, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maden, Ayse Dilek +3 more
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Journal of Function Spaces, 2023 There has been an upsurge of research on complex networks in recent years. The purpose of this paper is to study the mathematical properties of the random pentagonal chain networks PECn with the help of graph theory.
Jia-Bao Liu, Qing Xie, Jiao-Jiao Gu
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On Relation between the Kirchhoff Index and Laplacian-Energy-Like Invariant of Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-11/μi and LEL(G)=Σi=1n-1
Emina Milovanovic +2 more
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Results on Resistance Distance and Kirchhoff Index of Graphs With Generalized Pockets
Frontiers in Physics, 2022 F, Hv are considered simple connected graphs on n and m + 1 vertices, and v is a specified vertex of Hv and u1, u2, … uk ∈ F. The graph G = G[F, u1, … , uk, Hv] is called a graph with k pockets, obtained by taking one copy of F and k copies of Hv and ...
Qun Liu, Jiaqi Li
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