Selected topics on Wiener index. (English) Zbl 07926866
Summary: The Wiener index is defined as the sum of distances between all unordered pairs of vertices in a graph. It is one of the most recognized and well-researched topological indices, which is on the other hand still a very active area of research. This work presents a natural continuation of the paper [M. Knor et al., Ars Math. Contemp. 11, No. 2, 327–352 (2016; Zbl 1355.05099)] in which several interesting open questions on the topic were outlined. Here we collect answers gathered so far, give further insights on the topic of extremal values of Wiener index in different settings, and present further intriguing problems and conjectures.
MSC:
| 05C09 | Graphical indices (Wiener index, Zagreb index, Randić index, etc.) |
| 05C05 | Trees |
| 05C12 | Distance in graphs |
| 05C20 | Directed graphs (digraphs), tournaments |
| 05C92 | Chemical graph theory |
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
Keywords:
graph distance; Wiener index; average distance; topological index; molecular descriptor; chemical graph theoryReferences:
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