We explicitly compute the effective resistances between any two vertices of a prism graph by using circuit reductions and our earlier findings on a ladder graph. As an application, we derived a closed form formula for the Kirchhoff index of a prism graph. We show as a byproduct that an explicit sum formula involving trigonometric functions hold by comparing our formula for the Kirchhoff index and previously known results in the literature. We also expressed our formulas in terms of certain generalized Fibonacci numbers.
Effective Resistances, Kirchhoff index and Admissible Invariants of Ladder Graphs
On the resistance distance and Kirchhoff index of a linear hexagonal (cylinder) chain
Extremal octagonal chains with respect to the Kirchhoff index
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