Some Topological Indices Related to Paley Graphs

Document Type : Research Paper

Author

Department of Mathematics, Shoushtar branch, Islamic Azad University, Shoushtar, Iran

Abstract

Let ‎GF(q)‎ denote the finite field with ‎‎‎q‎ elements. The Paley graph ‎‎‎Paley(q)‎ is defined to be a graph with vertex set ‎‎ GF(q)‎ ‎‎ such that two vertices ‎‎a‎‎ and ‎‎b‎‎ are joined with an edge if ‎‎a-b ‎‎ is a non-zero square. If we assume ‎‎q‎≡‎1(mod4) ‎‎, then this graph is undirected. In this paper, our aim is to compute the topological indices of ‎‎ Paley(q)‎ ‎‎ such as the Wiener, PI and Szeged indices of this graph.

Keywords


  1. L. Carlitz, A theorem on permutations in a finite field, Proc. Amer. Math. Soc. 11 (1960) 456-459.
  2. M. R. Darafsheh, Computation of topological indices of some graphs, Acta Appl. Math. 110(2010) 1225-1235.‎
  3. C. D. Godsil and G. F. Royle, Algebraice Graph Theory, Grad. Texts in Math, 207, Springer-Verlag, New York,2001.
  4. B. Huppert, Endliche Gruppen I,‎Springer-Verlag, ‎Berlin, Heidelberg, 1967.‎
  5. G. A. Jones, ‎ Paley and the Paley Graphs, In: Jones G., Ponomarenko I., Širáň J. (eds) Isomorphisms, Symmetry and Computations in Algebraic Graph Theory. WAGT 2016. Springer Proceedings in Mathematics & Statistics  305, pp. 155−183,  Springer, Cham.
  6. R. E. A. C. Paley, ‎On ‎orthogonal ‎matrices, ‎J. Math. Phys. ‎12 (1933) ‎311-320.
  7. W. Peisert, ‎All ‎self-complementary ‎symmetric ‎graphs, ‎J. Algebra‎ 240 (2001) ‎209-229.‎
  8. ‎H. Wiener, ‎Structural ‎determination ‎of ‎paraffin ‎boiling ‎points, ‎J. Am. Chem. Soc. 69(1947)17‎-20.