The maximum hyper-Wiener index of cacti

Autor: Shang-wang Tan, Dong-fang Wang
Rok vydání: 2014
Předmět:
Zdroj: Journal of Applied Mathematics and Computing. 47:91-102
ISSN: 1865-2085
1598-5865
DOI: 10.1007/s12190-014-0763-8
Popis: The Wiener index of a connected graph \(G\) is the sum of distances between all unordered pairs of vertices in the graph. The hyper-Wiener index is defined as \(WW(G)= \frac{1}{2}\sum \nolimits _{\{u,v\} \subseteq V(G)}( d(u,v)+d^2 (u,v))\), where \(d(u,v)\) is the number of edges on a shortest path connecting vertices \(u\) and \(v\). A cactus graph is a connected graph in which each block is either an edge or a cycle. In the paper, we characterize the extremal cacti having the largest Wiener and hyper-Wiener indexes among all cacti with \(n\) vertices and \(r\) cycles.
Databáze: OpenAIRE
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