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The atom-bond connectivity index of chemical unicyclic graphs. (English) Zbl 1289.05244
Summary: The atom-bond connectivity (ABC) index of a graph $$G$$ is defined as the sum of the weights $$\left(\frac{d_u+d_v-2}{d_ud_v}\right)^\frac 12$$ of all edges $$uv$$ of $$G$$, where $$d_u$$ and $$d_v$$ denote the degrees of vertices $$u$$ and $$v$$ respectively in $$G$$. The ABC index provides a good model for the stability of linear and branched alkane as well as the strain energy of cycloalkanes. The sharp lower bounds on ABC index of chemical unicyclic graphs are obtained.
##### MSC:
 05C40 Connectivity 05C90 Applications of graph theory 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
##### Keywords:
atom-bond connectivity index; unicyclic graphs
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