Let G be a simple undirected connected graph. The resistance distance \(R_{G}(u,v)\) between two vertices u, v of G is equal to the effective resistance between the two points in the corresponding electrical network in which each edge of G is replaced by a unit resistor. The resistance spectrum \(\textrm{RS}(G)\) of G is defined as the multiset of resistance distances for all pairs of vertices in the graph. A graph G is said to be determined by the resistance spectrum if there is no non-isomorphic graph with the same resistance spectrum as G. Employing the principles of electrical networks and the local rules of resistance distance, this paper demonstrates that double starlike tree, sandglass graph, kite graph, pineapple graph, chained oxide network and friendship graph can be determined by their resistance spectra.
