Resistance Between Two Nodes of a Ring Clique Network

Li, Shuli; Tian, Tao

doi:10.1007/s00034-021-01859-7

Cited by 2 publications

(1 citation statement)

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“…It is interesting to note that a good deal of attention has been paid to resistance distances in plane networks, such as fullerene graphs [29], Möbius ladder graphs [28], ladder graphs [44], Apollonian network [41], Sierpinski Gasket Network [43], simple cubic network lattices [30], straight linear 2trees [38], Flower networks [42], Path Network [45], class of plane hexagonal networks [36], linear octogonal networks [16], and linear polyacene graphs [5]. Many formulae, such as combinatorial formulae, algebraic formulae, probabilistic formulae and so forth have been putforth for calculating resistance distance.…”

Section: Introductionmentioning

confidence: 99%

Resistance distance of generalized wheel and dumbbell graph using symmetric {1}-inverse of Laplacian matrix

Kaliyaperumal

Desikan

2023

Proyecciones (Antofagasta)

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A new class of graphs called dumbbell graphs, denoted by DB(Wm,n) is the graph obtained from two copies of generalized wheel graph Wm,n, m ≥ 2, n ≥ 3. It is a graph on 2 (m + n) vertices obtained by connecting m-vertices in one copy with the corresponding vertices in the other copy. The resistance distance between two vertices vi and vj, denoted by rij , is defined as the effective electrical resistance between them if each edge of G is replaced by 1 ohm resistor. The Kirchhoff index is the sum of the resistance distances between all pairs of vertices in the graph. In this paper, we formulate the resistance distance of Wm,n and DB(Wm,n) using Symmetric {1}-inverse of Laplacian matrices. We provide examples to illustrate the proposed method and also obtain the Kirchhoff indices for these examples.

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