On Equiresistant Graphs

We say a finite simple connected undirected graph is equiresistant if all its edges have the same effective resistance when the graph is considered as an electric circuit where the edges are unit resistors. Using simple properties of electric circuits, we identify some new families of graphs that are equiresistant and then apply this knowledge to find upper bounds for some molecular indices that improve; in the case of equiresistant graphs, similar upper bounds are found in the literature.