On Eccentric Connectivity Index of Eccentric Graph of Regular Dendrimer

The eccentric connectivity index $\xi ^c(G)$ of a connected graph G is defined as $\xi ^c(G) =\sum _{v \in V(G)}{deg(v) e(v)},$ where deg( v) is the degree of vertex v and e( v) is the eccentricity of v. The eccentric graph, $G_e$, of a graph G has the same set of vertices as G; with two vertices u; v adjacent in Ge if and only if either u is an eccentric vertex of v or v is an eccentric vertex of u: In this paper, we obtain a formula for the eccentric connectivity index of the eccentric graph of a regular dendrimer. We also derive a formula for the eccentric connectivity index for the second iteration of eccentric graph of regular dendrimer

The Eccentric Connectivity Index of Dendrimers

Abstract If G is a connected graph with vertex set V , then the eccentric connectivity index of G, ξ C (G), is defined as is the degree of a vertex v and ecc(v) is its eccentricity. We obtain exact formulas for calculating the eccentric connectivity index of dendrimers. Mathematics Subject Classification: 05C05, 05C1

A Note on Distance-Based Entropy of Dendrimers

This paper introduces a variant of entropy measures based on vertex eccentricity and applies it to all graphs representing the isomers of octane. Taking into account the vertex degree as well (degree-ecc-entropy), we find a good correlation with the acentric factor of octane isomers. In particular, we compute the degree-ecc-entropy for three classes of dendrimer graphs

The bounds for the distance two labelling and radio labelling of nanostar tree dendrimer

The distance two labelling and radio labelling problems are applicable to find the optimal frequency assignments on AM and FM radio stations. The distance two labelling, known as L(2,1)-labelling of a graph A, can be defined as a function, , from the vertex set V(A) to the set of all nonnegative integers such that (, ) represents the distance between the vertices c and s in where the absolute values of the difference between () and () are greater than or equal to both 2 and 1 if (, )=1 and (, ) = 2, respectively. The L(2,1)-labelling number of , denoted by 2,1 (), can be defined as the smallest number j such that there is an (2,1) −labeling with maximum label j. A radio labelling of a connected graph A is an injection k from the vertices of to such that (, ) + |() − ()| ≥ 1 + ∀ , ∈ (), where represents the diameter of graph . The radio numbers of and A are represented by () and () which are the maximum number assigned to any vertex of and the minimum value of () taken over all labellings k of , respectively. Our main goal is to obtain the bounds for the distance two labelling and radio labelling of nanostar tree dendrimers

Wiener Index Calculation on the Benzenoid System: A Review Article

The Weiner index is considered one of the basic descriptors of fixed interconnection networks because it provides the average distance between any two nodes of the network. Many methods have been used by researchers to calculate the value of the Wiener index. starting from the brute force method to the invention of an algorithm to calculate the Wiener index without calculating the distance matrix. The application of the Wiener index is found in the molecular structure of organic compounds, especially the benzenoid system. The value of the Wiener index of a molecule is closely related to its physical and chemical properties. This paper will show a comprehensive bibliometric survey of peer-reviewed articles referring to the Wiener index of benzenoid. The Wiener index values of several benzenoid compounds using cubic polynomial are also reported. The Wiener index of benzenoid supports much of the research and provides productive citations for citing the study.   Keywords: Wiener index, benzenoid, distance matrix, chemical properties, cubic polynomial, topological

Novel Strategies in Ischemic Heart Disease

The first edition of this book will provide a comprehensive overview of ischemic heart disease, including epidemiology, risk factors, pathogenesis, clinical presentation, diagnostic tests, differential diagnosis, treatment, complications and prognosis. Also discussed are current treatment options, protocols and diagnostic procedures, as well as the latest advances in the field. The book will serve as a cutting-edge point of reference for the basic or clinical researcher, and any clinician involved in the diagnosis and management of ischemic heart disease. This book is essentially designed to fill the vital gap existing between these practices, to provide a textbook that is substantial and readable, compact and reasonably comprehensive, and to provide an excellent blend of "basics to bedside and beyond" in the field of ischemic heart disease. The book also covers the future novel treatment strategies, focusing on the basic scientific and clinical aspects of the diagnosis and management of ischemic heart disease