let g be a connected simple (molecular) graph. the distance d(u, v) between two vertices u and v of g is equal to the length of a shortest path that connects u and v. in this paper we compute some distance based topological indices of h-phenylenic nanotorus. at first we obtain an exactformula for the wiener index. as application we calculate the schultz index and modified schultz index of this ...

For a graph G = (V,E), the modified Schultz index of G is defined as S∗(G) = ∑ {u,v}⊂V (G) (dG(u) · dG(v))dG(u, v) where dG(u) (or d(u)) is the degree of the vertex u of G, and dG(u, v) is the distance between u and v. Lower bounds on modified Schultz index in trees in terms of the order and diameter are determined. Mathematics Subject Classification: 05C05, 05C12

For a graph G = (V,E), the modified Schultz index of G is defined as S∗(G) = ∑ {u,v}⊆V (G) (dG(u) · dG(v))dG(u, v) where dG(u) (or d(u)) is the degree of the vertex u of G, and dG(u, v) is the distance between u and v. Let B(n) be the set of bicyclic graph with n vertices. In this paper, we study the modified Schultz index of B(n), graphs in B(n) with the smallest modified Schultz index S∗(G) a...

Let G be a connected simple (molecular) graph. The distance d(u, v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. In this paper we compute some distance based topological indices of H-Phenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...

The Wiener Index, or the Wiener Number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener Index for trees, and Ivan Gutman proposed a modification of the Schultz index with...

Abstract In this paper, the exact formulae for the Harary indices of join, disjunction, symmetric difference, strong product of graphs are obtained. Also, the Schultz and modified Schultz indices of join and strong product of graphs are computed. We apply some of our results to compute the Harary, Schultz and modified Schultz indices of fan graph, wheel graph, open fence and closed fence graphs.