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Vietnam Journal of Mathematics 33:3 (2005) 343-348 |
A Formula About Tree |
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Ahmed Ayache, Walied H. Sharif, and Vu Dinh Hoa |
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Abstract. Let $G$ be a tree. It is proved that for any vertex $v$ of $G$ $$ \vert V \vert +\sum_{q \in V}[d(q)-2]l(v,q)=1 $$ in which $d(q)$ is the degree of the vertex $q$, and $l(v,q)$ is the distance between $v$ and $q$ in $G$. This result enable us to derive a formula concering the average distance for some particular trees. |
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