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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.

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