BOUNDS FOR THE SCHULTZ MOLECULAR TOPOLOGICAL INDEX

We present some lower and upper bounds for the Schultz molecular topological index (MTI) in terms of the graph invariants such as the number of vertices, the number of edges, minimum vertex degree, maximum vertex degree, and the Wiener index. INTRODUCTION Let G be a connected simple graph with n vertices. The adjacency matrix A of G is an n× n matrix (Aij) such that Aij = 1 if the vertices i and j are adjacent and 0 otherwise. The distance matrix D of G is an n × n matrix (Dij) such that Dij is just the distance between the vertices i and j. The degree vi of the vertex i is the number of its first neighbors. The molecular topological index (MTI) of the graph G introduced by Schultz [1] in 1989 is defined as MTI = MTI(G) = n ∑