Resistance Distance and Kirchhoff Index for a Class of Graphs

WanJun Yin, ZhengFeng Ming, Qun Liu
2018 Mathematical Problems in Engineering  
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
more » ... e 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.
doi:10.1155/2018/1028614 fatcat:b2p3tmsyfzg5hdsueydr5y4wmi