Abstract
The resistance distances between any pair of vertices in a graph \(H\) are equal to the resistance distances between any pair of vertices on an electrical network, constructed to correspond to \(H,\) with each edge being replaced by a unit resistor. In this paper, we will discuss the resistance distances between two vertices of subdivided cyclic silicate network. A unit resistor \(1-\Omega\) is used to replace each edge. In this paper, the resistance distances between any arbitrary pairs of vertices of a subdivided cyclic silicate network are calculated using techniques from electrical network theory such as the parallel and series principles, the star-triangle transformation, the principle of elimination and substitution, and the delta-star transformation. The study of resistance distances in segmented cyclic silicate networks has far-reaching implications in materials science and computational chemistry.
