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Reseach Article

Wiener Index of Some Cycle Related Graphs using Matlab

by K. Thilakam, A. Sumathi
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 90 - Number 5
Year of Publication: 2014
Authors: K. Thilakam, A. Sumathi
10.5120/15574-4230

K. Thilakam, A. Sumathi . Wiener Index of Some Cycle Related Graphs using Matlab. International Journal of Computer Applications. 90, 5 ( March 2014), 47-50. DOI=10.5120/15574-4230

@article{ 10.5120/15574-4230,
author = { K. Thilakam, A. Sumathi },
title = { Wiener Index of Some Cycle Related Graphs using Matlab },
journal = { International Journal of Computer Applications },
issue_date = { March 2014 },
volume = { 90 },
number = { 5 },
month = { March },
year = { 2014 },
issn = { 0975-8887 },
pages = { 47-50 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume90/number5/15574-4230/ },
doi = { 10.5120/15574-4230 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:10:18.209561+05:30
%A K. Thilakam
%A A. Sumathi
%T Wiener Index of Some Cycle Related Graphs using Matlab
%J International Journal of Computer Applications
%@ 0975-8887
%V 90
%N 5
%P 47-50
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The Wiener index is one of the oldest molecular-graph-based structure-descriptors. It was first proposed by American Chemist Harold Wiener in 1947 as an aid to determine the boiling point of paraffin. The study of Wiener index is one of the current areas of research in mathematical chemistry. It also gives good correlations between Wiener index (of molecular graphs) and the physico-chemical properties of the underlying organic compounds. That is, the Wiener index of a molecular graph provides a rough measure of the compactness of the underlying molecule. The Wiener index W(G) of a connected graph G is the sum of the distances between all pairs (ordered) of vertices of G. In this paper, we give the program for calculating the Wiener index of Cata-condensed Cyclic graph and two cycles sharing their edges using MATLAB and discuss the coincidence of Wiener indices of Cata-condensed Cyclic graph with its characteristic graph and give the Wiener number for two Cycles sharing maximum and minimum number of edges.

References
  1. Andrey A. Dobrynin, Congruence Relations for the Wiener index of Hexagonal Chains, J. chem. Inf. Comput. Sci 1997, 37,1109-1110
  2. Andrey A. Dobrynin, New congruence Relations for Wiener index of Cata-Condensed Benzenoid Graphs, J. chem. Inf. Comput. Sci 1998, 38,405-409.
  3. Balakrishnan R and Ranganathan . K. M, A text Book of Graph Theory,Springer-Verlag, New York,2000
  4. Harary . F, Graph Theory (Addison –Wesley, Reading MA , 1971). J. chem. Inf. Comput. Sci 1997, 37,1109-1110.
  5. Mohar . B and Pisanski. T, How to compute the Wiener index of graph, J. Math. Chem. , 2(1988),267-277
  6. Sethuraman . G, Selvaraju. P, Gracefulness of arbitrary super subdivisions of graphs,, Indian J. pure appl. Math, 32(7):1059-1064,July 2001.
  7. Sridharan. N and Thilakam. K, Wiener number of super subdivisions of Pn, Cn, K1,n, Antarctica J. Math. ,8(3)(2011),199-211
  8. Thilakam K, Sumathi A, How to Compute the Wiener index of a graph using MATLAB, International Journal of Applied Mathematics& Statistical Sciences, Vol. 2, Issue 5, Nov 2013, 143-148.
  9. Thilakam. K, Sumathi A, Wiener Index of Arbitrary super subdivision of some cycle related graphs, Jamal Academic Research Journal,vol. 6. No. 2
  10. Thilakam. K, & Sumathi A, Wiener Number of Arbitrary Super Subdivisions of Wheel and Fan , Bulletin of Pure and Applied Sciences ,Volume 31 E –Math. & Stat. Issue-2(July-Dec) 2012, 211-216.
  11. Wiener. H , Structural determination of paraffin boiling points, J. Am chem . Soc. 69 (1947)17-20.
  12. http://mathworld. wolfram. com/WienerIndex
Index Terms

Computer Science
Information Sciences

Keywords

Cycle Distance Wiener index MATLAB