| Popis: |
The Harary index and Harary* index are defined as follows $H(G)=\sum_{k\geq1}\gamma(G,k)\frac{1}{k}$ and $H^{*}(G)=\sum_{k\geq1}\gamma(G,k)$, where $\gamma(G,k)$ be the number of vertex pairs of the graph $G$ that are at distance $k$. In this paper, the largest and smallest bound of the Harary index of trees with at most one generalized center vertex are determined. We give the formula of Harary$^{*}$ index of trees with at most one generalized center vertex and vertices number n, that is, H*(T)=\frac{(n+2)(n-1)}{4}$. And also give two conjectures with respective to Harary index and Harary* index in trees. |
