Abstract

In this note, we prove a graph inequality based on the sizes of the common neighborhoods. We also characterize the extremal graphs that achieve equality. The result was first discovered as a consequence of Foster’s classical theorem about electrical networks. We also present a short combinatorial proof that was inspired by a similar inequality related to the Turán’s celebrated theorem.

Full Text
Paper version not known

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 call

Disclaimer: 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.