Research ArticleOpen AccessGoogle Scholar indexed
Wiener Number of Some Subgraphs in Archimedean Tilings
Cheng Yi College, Jimei University, Xiamen, China
- 1 Cheng Yi College, Jimei University, Xiamen, China
Applied Mathematics·Volume 12 (2021)·Pages 939–946·Published 8 November 2021·DOI10.4236/am.2021.1211062
Copy link · social · email
Abstract
In this paper, we deduce Wiener number of some connected subgraphs in tilings (4, 4, 4, 4) and (4, 6, 12), which are in Archimedean tilings. And compute their average distance.
KeywordsArchimedean TilingWiener NumberBinary Hamming GraphAverage Distance
- Wiener, H. (1947) Structural Determination of Paraffin Boiling Points. Journal of the American Chemical Society, 69, 17-20. https://doi.org/10.1021/ja01193a005
- Banerjee, S., Nath, D. and Chaudhuri, B.K. (1982) Phenomenological Theory of the Isostructural Phase Transition in H-Bonded and with a Pseudospin Model. Physical Review B, 25, 1883. https://doi.org/10.1103/PhysRevB.25.1883
- Basak, S.C., Restrepo, G. and Villaveces, J.L. (2014) Advances in Mathematical Chemistry and Applications. Hentham Science e-book, Vol. 1.
- Bonchev, D. (2002) The Wiener Number, Some Applications and New Developments. In: Topology in Chemistry: Discrete Mathematics of Molecules. Woodhead Publishing, Chichester, 58-88. https://doi.org/10.1016/B978-1-898563-76-1.50008-1
- Diudea, M.V., Gutman, I. and Jantschi, L. (2001) Molecular Topology. Nova, Huntington.
- Dobrynin, A.A., Entringer, R. and Gutman, I. (2001) Wiener Index of Trees: Theory and Applications. Acta Applicandae Mathematica, 66, 211-249. https://doi.org/10.1023/A:1010767517079
- Shiu, W.C. and Lam, P.C.B. (1997) Wiener Numbers of Some Pericondensed Benzenoid Molecule Systems. Congrseeus Numerantium, 126, 113-124.
- Gutman, I., Yeh, Y.N., Lee, S.L. and Luo, Y.L. (1993) Some Recent Results in the Theory of the Wiener Number. Indian Journal of Chemistry, 32A, 651-661.
- Ng Lay Ling (2004) Tilings and Patterns. Honours Project, Department of Mathematics, National Univercity of Singapore.
- Klavzar, S., Gutman, I. and Mohar, B. (1995) Labeling of Benzenoid Systems which Reflects the Vertex-Distance Relations. Journal of Chemical Information and Computer Science, 35, 590-593. https://doi.org/10.1021/ci00025a030
- Gutman, I. and Klavzar, S. (1996) A Method for Calculating Wiener Numbers of Benzenoid Hydrocarbons. Models in Chemistry, 133, 389-399.
- Pan, Y.J., Xie, M.F. and Zhang, F.J. (2018) Partial Cubes and Archimedean Tilings. Acta Mathematicae Applicatae Sinica., 34, 782-791. https://doi.org/10.1007/s10255-018-0788-0