文摘
The atom–bond connectivity (ABC) index is a well-known degree-based molecular structure descriptor with a variety of chemical applications. In 2010 Graovac and Ghorbani introduced a distance-based analog of this index, the Graovac–Ghorbani (7e9d115a881665e80" title="Click to view the MathML source">GG) index, which yielded promising results when compared to analogous descriptors. In this paper, we investigate the structure of graphs that maximize and minimize the 7e9d115a881665e80" title="Click to view the MathML source">GG index. Specifically, we show that amongst all bipartite graphs, the minimum 7e9d115a881665e80" title="Click to view the MathML source">GG index is attained by a complete bipartite graph, while the maximum 7e9d115a881665e80" title="Click to view the MathML source">GG index is attained by a path or a cycle-like graph; the structure of the resulting graph depends on the number of vertices. Through the course of the research, we also derive an asymptotic estimate of the 7e9d115a881665e80" title="Click to view the MathML source">GG index of paths. In order to obtain our results, we introduce a normalized version of the 7e9d115a881665e80" title="Click to view the MathML source">GG index and call it the normalized Graovac–Ghorbani (7e8c0e90b0d6aa2743f273153544739" title="Click to view the MathML source">NGG) index. Finally, we discuss some related open questions as a potential extension of our work.