2021/08/18 by E. J. Evans, Evans, E. J., A. E. Francis +1 · 3 citations
Computer Science · Engineering · Mathematics · #05C12 #05C85 #05C90 #94C15 #Algorithm #Combinatorics #Combinatorics (math.CO) #Computer science #Distance matrix #FOS: Computer and information sciences #FOS: Mathematics #Graph #Graph theory #Graph theory and applications #Grid #Information Theory (cs.IT) #Line graph #Mathematics #Matrix (chemical analysis) #Molecular Junctions and Nanostructures #Ranging #Resistance distance #Telecommunications #Theoretical computer science #Topology (electrical circuits) #VLSI and FPGA Design Techniques #cs.IT #math.CO #math.IT #msc:05C12 #msc:05C85 #msc:05C90 #msc:94C15
paper · pdf · doi:10.48550/arxiv.2108.07942
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2021/08/18 · arxiv created 2021/09/13 · arxiv updated 2021/09/15 · openalex created_date 2022/10/04 · openalex updated_date 2026/08/05
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 of the technique. We also present some open questions and conjectures.