Exact Formula for Computing the Hyper-Wiener Index on Rows of Unit Cells of the Face-Centred Cubic Lattice

[1] A. Al-Kandari, P. Manuel, and I. Rajasingh, Wiener index of sodium chloride and benzenoid structures, The Journal of Combinatorial Mathe- matics and Combinatorial Computing 97 (2011), 33-42.Search in Google Scholar

[2] B. Bogdanov, S. Nikolić, and N. Trinajstić, On the three-dimensional Wiener number, Journal of Mathematical Chemistry 3 (1989), 299-309.10.1007/BF01169597Open DOISearch in Google Scholar

[3] B. Bollobfias, Graph theory. an introductory course, Springer-Verlag, New York, 1979.Search in Google Scholar

[4] G. Cash, S. Klavzar, and M. Petkovsek, Three methods for calculation of the hyper-Wiener index of molecular graphs, J. Chem. Inf. Comput. Sci. 42 (2002), 571-576.10.1021/ci0100999Open DOISearch in Google Scholar

[5] C. R. A. Catlow, Modelling and predicting crystal structures, Interdisci- plinary Science Reviews 40 (2015), no. 3, 294-307.Search in Google Scholar

[6] J. H. Conway and N. J. A. Sloane, Sphere packings, lattices, and groups, 2nd ed, Springer-Verlag, New York, 1993.10.1007/978-1-4757-2249-9Search in Google Scholar

[7] K. Ch. Das, N. Akgunes, M. Togan, A. Yurttas, I. N. Cangul, and A. S. Cevik, On the first Zagreb index and multiplicative Zagreb coindices of graphs, An. Sfitiintfi. Univ. \Ovidius" Constantfia Ser. Mat. 24 (2016), no. 1, 153-176.Search in Google Scholar

[8] A. A. Dobrynin, I. Gutman, S. Klavzar, and P. Zigert, Wiener index of hexagonal systems, Acta Applicandae Mathematicae 72 (2002), 247-294.10.1023/A:1016290123303Search in Google Scholar

[9] S. Klavzar and I. Gutman, Wiener number of vertex-weighted graphs and a chemical application, Discrete Applied Mathematics 80 (1995), 73-81.10.1016/S0166-218X(97)00070-XSearch in Google Scholar

[10] S. Klavzar, P. Zigerta, and I. Gutman, An algorithm for the calculation of the hyper-Wiener index of benzenoid hydrocarbons, Computers and Chem- istry 24 (2000), 229-233.10.1016/S0097-8485(99)00062-5Search in Google Scholar

[11] D. J. Klein, I. Lukovits, and I. Gutman, On the definition of the hyper- Wiener index for cycle-containing structures, J. Chem. Inf. Comput. Sci. 35 (1995), 50-52.10.1021/ci00023a007Open DOISearch in Google Scholar

[12] R. Klette and A. Rosenfeld, Digital geometry geometric methods for dig- ital picture analysis, Morgan Kaufmann, 2004.10.1016/B978-155860861-0/50005-5Search in Google Scholar

[13] P. Krishna and A. R. Verma, Closed packed structures, International Union of Crystallography, Chester, UK, 1981.Search in Google Scholar

[14] P. Manuel, I. Rajasingh, and M. Arockiaraj, Wiener and Szeged in- dices of regular tessellations, International Conference on Information and Network Technology (ICINT 2012) IPCSIT 37, IACSIT Press,Singapore (2012).Search in Google Scholar

[15] H. Mujahed and B. Nagy, Wiener index on rows of unit cells of the face- centred cubic lattice, Acta Crystallographica, Section A: Foundations and Advances A72 (2016), 243-249.10.1107/S205327331502274326919376Search in Google Scholar

[16] B. Nagy and R. Strand, Non-traditional grids embedded in Zn, Interna- tional Journal of Shape Modeling 47 (2008), 209-228.10.1142/S0218654308001154Search in Google Scholar

[17] R. H. Petrucci, W. S. Harwood, F. G. Herring, and J. D. Madura, General chemistry: Principles and modern applications. ninth edition, Pearson Education, Inc.g, New Jersey, 2007.Search in Google Scholar

[18] M. Randic, Novel molecular descriptor for structure-property studies, Chemical Physics Letters 211 (1993), 478-483.10.1016/0009-2614(93)87094-JSearch in Google Scholar

[19] N. J. A. Sloane (ed.), The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org, time of access: 04.04.2017Search in Google Scholar

[20] R. Strand and B. Nagy, Distances based on neighbourhood sequences in non-standard three-dimensional grids, Discrete Applied Mathematics 155 (2007), 548-557.10.1016/j.dam.2006.09.005Search in Google Scholar

[21] R. Strand and B. Nagy, Path-based distance functions in n-dimensional generalizations of the face-and body-centered cubic grids, Discrete Applied Mathematics 157 (2009), 3386-3400.10.1016/j.dam.2009.02.008Search in Google Scholar

[22] R. Strand, B. Nagy, and G. Borgefors, Digital distance functions on three- dimensional grids, Theoretical Computer Science 412 (2011), 1350-1363.10.1016/j.tcs.2010.10.027Search in Google Scholar

[23] H. Wiener, Structural determination of parafin boiling points, Journal of American Chemical Society 69 (1947), 17-20.10.1021/ja01193a00520291038Search in Google Scholar

[24] R. Xing, B. Zhou, and X. Qi, HyperWiener index of unicyclic graphs, MATCH Communications in Mathematical and in Computer Chemistry 66 (2011), 315-328.Search in Google Scholar