Results 11 to 20 of about 3,634,246 (271)
On the Kirchhoff matrix, a new Kirchhoff index and the Kirchhoff energy [PDF]
Journal of Inequalities and Applications, 2013 The main purpose of this paper is to define and investigate the Kirchhoff matrix, a new Kirchhoff index, the Kirchhoff energy and the Kirchhoff Estrada index of a graph. In addition, we establish upper and lower bounds for these new indexes and energy. In the final section, we point out a new possible application area for graphs by considering this new
CANGÜL, İSMAİL NACİ +3 more
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Symmetry, 2023 Several topological indices are known to have widespread implications in a variety of research areas. Over the years, the Kirchhoff index has turned out to be an extremely significant and efficient index. In this paper, we propose the exact formulas for the expected values of the random polyomino chain to construct the multiplicative degree-Kirchhoff ...
Meilian Li +4 more
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Journal of Mathematics, 2022 It is well known that many topological indices have widespread use in lots of fields about scientific research, and the Kirchhoff index plays a major role in many different sectors over the years. Recently, Li et al. (Appl. Math. Comput.
Jia-Bao Liu +3 more
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Enumeration of the Additive Degree–Kirchhoff Index in the Random Polygonal Chains
Axioms, 2022 The additive degree–Kirchhoff index is an important topological index. This paper we devote to establishing the explicit analytical expression for the simple formulae of the expected value of the additive degree–Kirchhoff index in a random polygon. Based
Xianya Geng, Wanlin Zhu
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The Kirchhoff Index of Hypercubes and Related Complex Networks [PDF]
Discrete Dynamics in Nature and Society, 2013 The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor.
Jiabao Liu +3 more
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Extremal polygonal chains with respect to the Kirchhoff index [PDF]
Discrete Applied Mathematics, 2023 13 pages.
Ma, Qi
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The Extremal Cacti on Multiplicative Degree-Kirchhoff Index
Mathematics, 2019 For a graph G, the resistance distance r G ( x , y ) is defined to be the effective resistance between vertices x and y, the multiplicative degree-Kirchhoff index R ∗ ( G ) = ∑ { x , y } ⊂ V ( G ) d G ( x ) d G
Fangguo He, Zhongxun Zhu
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Upper and Lower Bounds for the Kirchhoff Index of the n-Dimensional Hypercube Network
Complexity, 2020 The hypercube Qn is one of the most admirable and efficient interconnection network due to its excellent performance for some practical applications. The Kirchhoff index KfG is equal to the sum of resistance distances between any pairs of vertices in ...
Jia-Bao Liu +4 more
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The minimum Kirchhoff index of phenylene chains
Discrete Applied Mathematics, 2023 Let $G$ be a connected graph. The resistance distance between any two vertices of $G$ is equal to the effective resistance between them in the corresponding electrical network constructed from $G$ by replacing each edge with a unit resistor. The Kirchhoff index is defined as the sum of resistance distances between all pairs of the vertices.
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Concentration of the Kirchhoff index for Erdős–Rényi graphs [PDF]
Systems & Control Letters, 2014 Given an undirected graph, the resistance distance between two nodes is the resistance one would measure between these two nodes in an electrical network if edges were resistors. Summing these distances over all pairs of nodes yields the so-called Kirchhoff index of the graph, which measures its overall connectivity.
Nicolas Boumal, Xiuyuan Cheng
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