Resistance distance in subdivision-vertex join and subdivision-edge join of graphs

Bu, Changjiang; Yan, Bo; Zhou, Xueyan; Zhou, Jiang

doi:10.1016/j.laa.2014.06.018

Cited by 51 publications

(56 citation statements)

References 10 publications

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“…[13,33,34] Motivated by the results, in this paper, we further obtain generalized inverse representation for Laplacian matrices of subdivision-vertex and subdivision-edge corona graphs. The resistance distances of any pair of vertices in G 1 G 2 and G 1 G 2 can be obtained by the proposed approach.…”

Section: B(g) T B(g) = 2i M + A(l(g))mentioning

confidence: 93%

“…[8] The resistance distances attracted extensive attention of numerous mathematicians, due to its wide applications. [9][10][11][12][13][14] For more information on resistance distances of graphs, the readers are referred to the most recent papers. [15][16][17][18][19][20][21][22][23][24][25][26][27][28] It is of interest to study some graph operations, such as the Cartesian product, the Kronecker product, the corona, the edge corona, etc.…”

Section: B(g) T B(g) = 2i M + A(l(g))mentioning

confidence: 99%

“…Definition 2.2: (see [13]) Given a square matrix A, the group inverse of A, denoted by A # , is the unique matrix X that satisfies matrix equations…”

Section: Generalized Inverse and Kronecker Productmentioning

confidence: 99%

“…For more information, readers are referred to [13,38]. It is known that resistance distances in a connected graph G can be obtained from any {1}-inverse of L(G) according to the following lemma (see [13]). Lemma 2.1: (see [13]) Let G be a connected graph, and (L(G)) ij denote the (i, j)-entry of L(G).…”

Section: Lemmasmentioning

confidence: 99%

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The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications

Liu

Pan

2016

Linear and Multilinear Algebra

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Section: B(g) T B(g) = 2i M + A(l(g))mentioning

confidence: 93%

Section: B(g) T B(g) = 2i M + A(l(g))mentioning

confidence: 99%

“…Definition 2.2: (see [13]) Given a square matrix A, the group inverse of A, denoted by A # , is the unique matrix X that satisfies matrix equations…”

Section: Generalized Inverse and Kronecker Productmentioning

confidence: 99%

Section: Lemmasmentioning

confidence: 99%

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The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications

Liu

Pan

2016

Linear and Multilinear Algebra

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“…Our motivation to define such joins comes from [13] in which the author defined the subdivision-vertex join and the subdivision-edge join based on the subdivision graph [9,10]. The resistance distances of subdivision-vertex join and subdivision-edge join were obtained in [7].…”

Section: Discussionmentioning

confidence: 99%

Resistance distance and Kirchhoff index of R-vertex join and R-edge join of two graphs

Liu

Zhou

2015

Discrete Applied Mathematics

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Semi-Lipschitz functions and machine learning for discrete dynamical systems on graphs

Falciani

Pérez

2022

Mach Learn

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Consider a directed tree $${\mathcal {U}}$$ U and the space of all finite walks on it endowed with a quasi-pseudo-metric—the space of the strategies $${\mathcal {S}}$$ S on the graph,—which represent the possible changes in the evolution of a dynamical system over time. Consider a reward function acting in a subset $${\mathcal {S}}_0 \subset {\mathcal {S}}$$ S 0 ⊂ S which measures the success. Using well-known facts of the theory of semi-Lipschitz functions in quasi-pseudo-metric spaces, we extend the reward function to the whole space $${\mathcal {S}}.$$ S . We obtain in this way an oracle function, which gives a forecast of the reward function for the elements of $${\mathcal {S}}$$ S , that is, an estimate of the degree of success for any given strategy. After explaining the fundamental properties of a specific quasi-pseudo-metric that we define for the (graph) trees (the bifurcation quasi-pseudo-metric), we focus our attention on analyzing how this structure can be used to represent dynamical systems on graphs. We begin the explanation of the method with a simple example, which is proposed as a reference point for which some variants and successive generalizations are consecutively shown. The main objective is to explain the role of the lack of symmetry of quasi-metrics in our proposal: the irreversibility of dynamical processes is reflected in the asymmetry of their definition.

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Resistance distance in subdivision-vertex join and subdivision-edge join of graphs

Cited by 51 publications

References 10 publications

The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications

The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications

Resistance distance and Kirchhoff index of R-vertex join and R-edge join of two graphs

Semi-Lipschitz functions and machine learning for discrete dynamical systems on graphs

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