Abstract
The calculation of two-point resistance and the number of spanning trees of a resistor network is a classic problem in electric circuit theory, which has been studied extensively by many mathematicians and physicists for many years. Ge (2021) obtained the formulae for the resistance distances and the number of spanning trees in a complete bipartite graph plus a matching. In this paper, we give a so-called complete multipartite graph-blossomed star transformation which is similar to the mesh-star transformation in electrical networks. As applications, we obtain the close formulae of resistance distances and the number of spanning trees in a complete multipartite graph adding a matching. We also derive the formulae of the resistance distances in the almost complete graph, which is obtained from a complete graph by deleting a forest in which each component is a star.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
