By Kexiang Xu, Kinkar Ch. Das, Nenad Trinajstić (auth.)

This is the 1st booklet to target the topological index, the Harary index, of a graph, together with its mathematical homes, chemical functions and a few comparable and tasty open difficulties. This publication is devoted to Professor Frank Harary (1921—2005), the grandmaster of graph thought and its functions. It has be written by way of specialists within the box of graph concept and its purposes. For a attached graph G, as a massive distance-based topological index, the Harary index H(G) is outlined because the sum of the reciprocals of the space among any unordered vertices of the graph G. during this ebook, the authors file at the latest effects at the Harary index of a graph. those effects as a rule crisis exterior graphs with admire to the Harary index; the kin to different topological indices; its houses and purposes to natural graph thought and chemical graph conception; and major editions, i.e., additively and multiplicatively weighted Harary indices. within the final bankruptcy, we current a few open difficulties regarding the Harary index. As such, the publication won't simply be of curiosity to graph researchers, yet to mathematical chemists as well.