Resistance Distance and Kirchhoff Index for a Class of Graphs
Let G[F,Vk,Hv] be the graph with k pockets, where F is a simple graph of order n≥1, Vk={v1,v2,…,vk} is a subset of the vertex set of F, Hv is a simple graph of order m≥2, and v is a specified vertex of Hv. Also let G[F,Ek,Huv] be the graph with k edge pockets, where F is a simple graph of order n≥2, Ek={e1,e2,…ek} is a subset of the edge set of F, Huv is a simple graph of order m≥3, and uv is a specified edge of Huv such that Huv-u is isomorphic to Huv-v. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of G[F,Vk,Hv] and G[F,Ek,Huv] in terms of the resistance distance and Kirchhoff index F, Hv and F, Huv, respectively.
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2017 ◽
Vol 60
(1)
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pp. 197-205
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2015 ◽
Vol 70
(6)
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pp. 459-463
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2021 ◽
Vol 2021
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pp. 1-9
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2020 ◽
Vol 558
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pp. 124999
2020 ◽
Vol 12
(06)
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pp. 2050083