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On general Randić indices. (English) Zbl 1193.92089
Let $\alpha$ be a real number. The general Randić index of a graph $G$ is defined as $R_{\alpha}(G)=\sum_{i\sim j}(d_id_j)^{\alpha}$, where $d_i$ denotes the degree of the vertex $i$ in $G$, and summation goes over all pairs of adjacent vertices $i,j$. The authors investigate bounds for $R_{\alpha}(G)$ in the case when $\vert \alpha\vert >1$ and obtain some new results. (The case $\vert \alpha\vert \leq1$ has already been studied in the literature.)

92E10Molecular structures
05C90Applications of graph theory