Topological Indices of Certain Graphs

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

2 School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

10.22052/ijmc.2022.243381.1602

Abstract

In this paper we first consider and study certain edge-transitive connected graphs, such as the Hamming graphs, the Paley graphs and the Boolean lattice. Then as a consequence, we obtain the Wiener and the hyper-Wiener indices of these graphs.

Keywords


  1. R. Darafsheh, Computation of topological indices of some graphs, Acta Appl. Math. 110 (3) (2010) 1225-1235.
  2. R. Darafsheh, M. H. Khalifeh and H. Jolany, The hyper-Wiener index of one pentagonal carbon nanocone, Current Nanoscience 9 (4) (2013) 557-560.
  3. Godsil and G. Royle, Algebraic Graph Theory, Vol. 207 of Graduate Texts in Mathematics. Springer Verlag, New York – Heidelberg – Berlin, 2001.
  4. A. Jones, Paley and the Paley graphs, Isomorphisms, symmetry and computations in algebraic graph theory, Springer Proc. Math. Stat., 305, Springer, Cham, (2020) 155-183.
  5. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi, The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (5) (2008) 1402-1407.
  6. 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.
  7. M. Mirafzal and M. Ziaee, A note on the automorphism group of the Hamming graph, Trans. Combin. 10 (2) (2021) 129-136.
  8. Modabernia, Some topological indices related to Paley graphs, Iranian J. Math. Chem. 11 (2) (2020) 107-112.
  9. Sabidussi, On a class of fixed-point-free graphs, Proc. Amer. Math. Soc. 9 (1958) 800-804.
  10. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17-20.