A graph inequality on the common neighbourhood
Combinatorics
2019-12-03 v1
Abstract
In this note we prove a graph inequality based on the sizes of the common neighbourhoods. We also characterize the extremal graphs that achieve the equality. The result was first discovered as a consequence of the classical Forster's theorem in electric networks. We also present a short combinatorial proof that was inspired by a similar inequality related to the celebrated Tur\'an's theorem.
Keywords
Cite
@article{arxiv.1912.00417,
title = {A graph inequality on the common neighbourhood},
author = {Xiaomin Chen and Fenglin Huang and Shuhan Zhou and Mingxuan Zou and Junchi Zuo},
journal= {arXiv preprint arXiv:1912.00417},
year = {2019}
}