Wiener and Hyper-Wiener Indices of Polygonal Cylinder and Torus

In this study, we first introduce polygonal cylinder and torus using Cartesian products and topologically identifications and then find their Wiener and hyper-Wiener indices using a quick, interesting technique of counting. Our suggested mathematical structures could be of potential interests in representation of computer networks and enhancing lattice hardware security.

[1]  Wolfgang Linert,et al.  Trees with Extremal Hyper-Wiener Index: Mathematical Basis and Chemical Applications , 1997, J. Chem. Inf. Comput. Sci..

[2]  Wolfgang Linert,et al.  A Novel Definition of the Hyper-Wiener Index for Cycles , 1994, J. Chem. Inf. Comput. Sci..

[3]  István Lukovits,et al.  On the Definition of the Hyper-Wiener Index for Cycle-Containing Structures , 1995, J. Chem. Inf. Comput. Sci..

[4]  Gordon G. Cash,et al.  Three Methods for Calculation of the Hyper-Wiener Index of Molecular Graphs , 2002, J. Chem. Inf. Comput. Sci..

[5]  The Hyper-Wiener Index of One-pentagonal Carbon Nanocone , 2012, 1212.4411.

[6]  I. Gutman,et al.  Some recent results in the theory of the Wiener number , 1993 .

[7]  Ante Graovac,et al.  Topological Approach to the Chemistry of Conjugated Molecules , 1977 .

[8]  M. Randic Novel molecular descriptor for structure—property studies , 1993 .

[9]  Hua Wang,et al.  All but 49 Numbers are Wiener Indices of Trees , 2006 .

[10]  H. Wiener Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[11]  Ali Reza Ashrafi,et al.  The hyper-Wiener index of graph operations , 2008, Comput. Math. Appl..

[12]  H. Wiener Correlation of Heats of Isomerization, and Differences in Heats of Vaporization of Isomers, Among the Paraffin Hydrocarbons , 1947 .

[13]  Stephan Wagner A Class of Trees and its Wiener Index , 2006 .

[14]  Hongbo Hua,et al.  Wiener index, Harary index and Hamiltonicity of graphs , 2016, 1609.00114.

[15]  Hongbo Hua,et al.  On Harary Index and Traceable Graphs , 2013 .

[16]  H. Wiener,et al.  Influence of Interatomic Forces on Paraffin Properties , 1947 .

[17]  P. Jurs,et al.  Chemical Applications of Graph Theory: Part I. Fundamentals and Topological Indices. , 1988 .

[18]  István Lukovits,et al.  Correlation between components of the Wiener index and partition coefficients of hydrocarbons , 1992 .

[19]  H. Wiener Relation of the physical properties of the isomeric alkanes to molecular structure; surface, tension, specific dispersion, and critical solution temperature in aniline. , 1948, The Journal of physical and colloid chemistry.

[20]  M. Farahani ON THE SCHULTZ POLYNOMIAL AND HOSOYA POLYNOMIAL OF CIRCUMCORONENE SERIES OF BENZENOID , 2013 .

[21]  Mircea V. Diudea Wiener and Hyper-Wiener Numbers in a Single Matrix , 1996, J. Chem. Inf. Comput. Sci..

[22]  H. Wiener Vapor pressure-temperature relationships among the branched paraffin hydrocarbons. , 1948, The Journal of physical and colloid chemistry.

[23]  Dennis H. Rouvray,et al.  The modeling of chemical phenomena using topological indices , 1987 .

[24]  Xiaofeng Guo,et al.  Wiener matrix: Source of novel graph invariants , 1993, J. Chem. Inf. Comput. Sci..

[25]  I. Gutman,et al.  Mathematical Concepts in Organic Chemistry , 1986 .

[26]  István Lukovits Decomposition of the Wiener topological index. Application to drug–receptor interactions , 1988 .