Extremal linear triangular chains with respect to the Kirchhoff index

Abstract Let G be a connected graph. The resistance distance among two vertices is defined as the effective resistance between the corresponding nodes in the electrical network constructed from G by replacing each edge with a unit resistor. The Kirchhoff index is an important distance-based topological index corresponding to graphs, which is the sum of all the resistance distances pairs of G . Let B n be a linear polyomino chain with n squares. The linear triangular chain is a graph with 2 n triangles, characterized by randomly adding an edge to each square of B n so as to make it into two triangular faces. In this paper, by standard techniques of electrical networks and the recursion formula for resistance distances, we characterize the linear triangular chains with extreme Kirchhoff index.