Algorithmic techniques for finding resistance distances on structured graphs

In this paper, we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in combinatorial matrix theory and spectral graph theory. Moreover resistance distance has applications ranging from quantifying biological structures, distributed control systems, network analysis, and power grid systems. In this paper, we discuss both exact techniques and approximate techniques and for each method discussed we provide an illustrative example. We also present some open questions and conjectures. (C) 2022 Elsevier B.V. All rights reserved.