Computation of resistance distance and Kirchhoff index of chain of triangular bipyramid hexahedron

Abstract

The two point effective resistance in some electrical networks has been extensively studied by many mathematicians and physicists. The computation of the effective resistance among two points in a network is a well-known problem in electrical networks theory. To solve this problem, we can apply methods such as the series principle, parallel principle, star-mesh transformation and Delta-Y transformation. The resistance distance among vertices u and v in a graph G is the effective resistance among the corresponding points in the given electrical network obtained from G by converting each edge of G with resistor of 1 ohm. The Kirchhoff index is the sum of resistance distance between all pairs of vertices of graph G. Chain of triangular bipyramid hexahedron structure which is a polyhedral graph has many applications in the area of reticular chemistry. In our paper, we compute the resistance distance among all pairs of vertices in the chain of triangular bipyramid hexahedron. Also we compute the closed formula for Kirchhoff index.