The second-minimum Wiener index of cacti with given cycles
| Autor: | G. C. Keerthi Vasan, Selvaraj Balachandran, Hanyuan Deng |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Computer Science::Information Retrieval
General Mathematics Astrophysics::Instrumentation and Methods for Astrophysics 0211 other engineering and technologies Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 021107 urban & regional planning 0102 computer and information sciences 02 engineering and technology Wiener index 01 natural sciences Combinatorics 010201 computation theory & mathematics Cactus Computer Science::General Literature Connectivity Mathematics |
| Zdroj: | Asian-European Journal of Mathematics. 14:2150039 |
| ISSN: | 1793-7183 1793-5571 |
| DOI: | 10.1142/s179355712150039x |
| Popis: | The Wiener index [Formula: see text] of a connected graph [Formula: see text] is the sum of distances between all pairs of vertices of [Formula: see text]. A connected graph [Formula: see text] is said to be a cactus if each of its blocks is either a cycle or an edge. Let [Formula: see text] be the set of all [Formula: see text]-vertex cacti containing exactly [Formula: see text] cycles. Liu and Lu (2007) determined the unique graph in [Formula: see text] with the minimum Wiener index. Gutman, Li and Wei (2017) determined the unique graph in [Formula: see text] with maximum Wiener index. In this paper, we present the second-minimum Wiener index of graphs in [Formula: see text] and identify the corresponding extremal graphs, which solve partially the problem proposed by Gutman et al. [Cacti with [Formula: see text]-vertices and [Formula: see text] cycles having extremal Wiener index, Discrete Appl. Math. 232 (2017) 189–200] in 2017. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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