The Schultz and the Modified Schultz Indices of Kragujevac Trees

Document Type : Research Paper


Arak Uinversity of Technology, Arak, Iran.


Let G be simple connected graph with the vertex and edge sets V(G) and E(G), respectively. The Schultz and Modified Schultz indices of a connected graph G are defined as Sc(G) =1/2 ∑u,v∈V(G) (du + dv)d(u,v) and Sc*(G) = 1\2∑u,v∈ V(du×dv)d(u, v), where d(u, v) is the topological distance between vertices u and v, dv is the degree of vertex v of G. In this paper, computation of the Schultz and Modified Schultz indices of the Kragujevac trees is proposed. As application, we obtain an upper bound and a lower bound for the Schultz and the modified Schultz indices of this tree.


  1. I. Gutman, Selected properties of the Schultz molecular topological index, J. Chem. Inform. Comput. Sci. 34, 1087–1089 (1994).
  2. M. Randiĉ, Novel molecular descriptor for structure-property studies, Chemical Physics Letters, 211(4), 478fi-483 (1993).
  3. H.P. Schultz, Topological Organic Chemistry .1. Graph Theory and Topological Indices of Alkanes. J. Chem. Inf. Comput. Sci. 29, 227–228 (1989).
  4. S. Klavẑar, and I. Gutman, A Comparison of the Schultz Molecular Topological Index with the Wiener Index. J. Chem. Inf. Comput. Sci. 36, 1001–1003 (1996).
  5. B. Furtula, I. Gutman, M. Ivanović and D. Vukićević, Computer search for trees with minimal ABC index, Appl. Math. Comput. 219, 767–772 (2012).
  6. I. Gutman and B. Furtula, Trees with smallest atom-bond connectivity index, MATCH Commun. Math. Comput. Chem. 68, 131–136 (2012).
  7. I. Gutman, B. Furtula and M. Ivanovific, Notes on trees with minimal atom-bond connectivity index, MATCH Commun. Math. Com- put. Chem. 67, 467–482 (2012).
  8. R. Cruz, I. Gutman, J. Rada, Topological indices of Kragujevac trees, Proyecciones Journal of Mathematics, 33(4), 471–482 (2012).