What question did this study set out to answer?

The research aims to identify families of equiresistant graphs and explore their implications on molecular indices.

February 28, 2026Open Access

On Equiresistant Graphs

Key Points

The research aims to identify families of equiresistant graphs and explore their implications on molecular indices.
Analyzing properties of electric circuits to define equiresistant graphs.
Identifying new families of equiresistant graphs.
Applying findings to derive upper bounds for molecular indices.
Identified several new families of equiresistant graphs.
Established upper bounds for molecular indices that surpass previous literature findings.

Abstract

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.

On Equiresistant Graphs

Key Points

Abstract

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