Extremal octagonal chains with respect to the Kirchhoff index

Abstract

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. These indices have been computed for many interesting graphs, such as linear polyomino chain, linear/M\"{o}bius/cylinder hexagonal chain, and linear/M\"{o}bius/cylinder octagonal chain. In this paper, we characterized the maximum and minimum octagonal chains with respect to the Kirchhoff index.