Foster, Turán, and neighbors. (English) Zbl 1455.05019
Summary: 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.
MSC:
| 05C12 | Distance in graphs |
| 05C35 | Extremal problems in graph theory |
| 05C09 | Graphical indices (Wiener index, Zagreb index, Randić index, etc.) |
References:
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