The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ ...

The energy of a graph G as chemical concept leading to HMO theory was introduced by Hückel in 1931 and developed into mathematical interpretation many years later when Gutman 1978 gave his famous definition the sum absolute values eigenvalues adjacency matrix G. One general requirements for any topological index is that similar molecules have close TI values, which called smoothness. To explore...

On page 144 of (3], a (see Gutman[l]), formulated as follows:

Since the studies of Gutman and Gutman (2, 3), measurements of the serum acid phosphatase have become a recognized and widely used ancillary procedure for the diagnosis of cancer of the prostate and a practical means for the evaluation of the functional status of the tumor in many patients with metastasizing cancer of the prostate. While an abnormally increased value of serum acid phosphatase i...

Faculty of Civil and Environmental Engineering P-O Gutman 2004-02-20 Abstract When using the Pontryagin Maximum Principle in optimal control problems, the most difficult part of the numerical solution is associated with the non-linear operation of the maximization of the Hamiltonian over the control variables. For a class of problems, the optimal control vector is a vector function with continu...

Let G be a simple graph with the vertex set V(G) and edge set E(G) respectively. The degree of a vertex v in G is the number of vertices in G which are connected to v by an edge and denoted by dG(v). A topological index is a graph invarient which is numerical parameter obtained from a graph which characterize its topology.Thus for two isomorphic graphG and H the value of a particular topologica...