Abstract
We regard a graph as an electrical network where every edge is a resistance of 1 ohm. We show that, for an infinite graph of linear growth, Kirchhoff's laws combined with the finite power condition ensures the existence and uniqueness of an electric current when a current generator is added. We also show that the effective resistance between any two adjacent vertices in an infinite edge-transitive d-regular graph of moderate growth is 2 d , a result which has been expected by electrical engineers, but has previously been proved rigorously only in special cases.
Sign-in/Register to access full text options 
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.
