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The atom-bond connectivity index of chemical bicyclic graphs. (English) Zbl 1265.05354
Summary: The atom-bond connectivity (ABC) index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes, which is defined as ABC$$(G) =\sum\limits_{uv\in E(G)}\sqrt{\frac{d_u+d_v-2}{d_ud_v}}$$, where $$d_u$$ denotes the degree of a vertex $$u$$ in $$G$$. A chemical graph is a graph in which no vertex has degree greater than 4. In this paper, we obtain the sharp upper and lower bounds on ABC index of chemical bicyclic graphs.

##### MSC:
 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C40 Connectivity 05C07 Vertex degrees 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
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