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A formula about tree. (English) Zbl 1116.05018

Summary: Let \(G\) be a tree. We prove that for any vertex \(v\) of \(G\) \[ |V|+ \sum_{q\in V}[d(q)-2]l(v,q)=1 \] where \(d(q)\) is the degree of the vertex \(q\), and \(l(v,q)\) is the distance between \(v\) and \(q\) in \(G\). This result enables us to derive a formula concering the average distance for some particular trees.

MSC:

05C05 Trees
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