Research ArticleOpen AccessGoogle Scholar indexed
Reciprocal Complementary Wiener Numbers of Non-Caterpillars
Department of Applied Mathematics, South China Agricultural University, Guangzhou, China
Department of Applied Mathematics, South China Agricultural University, Guangzhou, China
Department of Applied Mathematics, South China Agricultural University, Guangzhou, China
- 1 Department of Applied Mathematics, South China Agricultural University, Guangzhou, China
- 2 Department of Applied Mathematics, South China Agricultural University, Guangzhou, China
- 3 Department of Applied Mathematics, South China Agricultural University, Guangzhou, China
Applied Mathematics·Volume 07 (2016)·Pages 219–226·Published 24 February 2016·DOI10.4236/am.2016.73020
Copy link · social · email
Abstract
The reciprocal complementary Wiener number of a connected graph G is defined as where is the vertex set. is the distance between vertices u and v , and d is the diameter of G . A tree is known as a caterpillar if the removal of all pendant vertices makes it as a path. Otherwise, it is called a non-caterpillar. Among all n -vertex non-cater- pillars with given diameter d , we obtain the unique tree with minimum reciprocal complementary Wiener number, where . We also determine the n -vertex non-caterpillars with the smallest, the second smallest and the third smallest reciprocal complementary Wiener numbers.
KeywordsReciprocal Complementary Wiener NumberWiener NumberCaterpillar
- Ivanciuc, O. (2003) Graph Theory in Chemistry. In: Gasteiger, J., Ed., Handbook of Chemoinformatics, Wiley-VCH. Weinheim, 103-138. http://dx.doi.org/10.1002/9783527618279.ch6
- Ivanciuc, O. (2003) Topological Indices. In: Gasteiger, J., Ed., Handbook of Chemoinformatics, Wiley-VCH, Weinheim, 981-1003. http://dx.doi.org/10.1002/9783527618279.ch36
- Janezic, D., Milicevic, A., Nikolic, S. and Trinajstic, N. (2007) Graph-Theoretical Matrices in Chemistry. University of Kragujevac, Kragujevac.
- Luo, W. and Zhou, B. (2009) On Ordinary and Reverse Wiener Indices of Non-Caterpillars. Mathematical and Computer Modelling, 50, 188-193. http://dx.doi.org/10.1016/j.mcm.2009.02.010
- Ivanciuc, O. (2000) QSAR Comparative Study of Wiener Descriptors for Weighted Molecular Graphs. Journal of Chemical Information and Modeling, 40, 1412-1422. http://dx.doi.org/10.1021/ci000068y
- Ivanciuc, O., Ivanciuc, T. and Balaban, A.T. (2000) The Complementary Distance Matrix, a New Molecular Graph Metric. ACH-Models in Chemistry, 137, 57-82.
- Ivanciuc, O., Ivanciuc, T. and Balaban, A.T. (2002) Quantitative Structure-Property Relationship Evaluation of Structural Descriptors Derived from the Distance and Reverse Wiener Matrices. Internet Electron. Journal of Computer-Aided Molecular Design, 1, 467-487.
- Ivanciuc, O., Ivanciuc, T. and Balaban, A.T. (1999) Vertex- and Edge-Weighted Molecular Graphs and Derived Structural Descriptors. In: Devillers, J. and Balaban, A.T., Eds., Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, 169-220.
- Cai, X. and Zhou, B. (2009) Reciprocal Complementary Wiener Numbers of Trees, Unicyclic Graphs and Bicyclic Graphs. Discrete Applied Mathematics, 157, 3046-3054. http://dx.doi.org/10.1016/j.dam.2009.05.001
- Zhou, B., Cai, X. and Trinajstic, N. (2009) On Reciprocal Complementary Wiener Number. Discrete Applied Mathematics, 157, 1628-1633. http://dx.doi.org/10.1016/j.dam.2008.09.010