(Received May 2, 2012) Graph theoretic fullerenes are designed to model large carbon molecules: each vertex represents a carbon atom and the edges represent chemical bonds. A totally symmetric Kekulé structure in a fullerene is a set of independent edges which is fixed by all symmetries of the fullerene. It was suggested in a paper by S.J.Austin, J.Baker, P.W.Fowler, D.E.Manolopoulos and in a p...

Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric−arithmetic index of graphs, Iran. J. Math Chem., 1 (2010) 17−27, in this paper we present lower and upper bounds on the third geometric−arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus−Gaddum−type result for GA3.

(24) Ritter, G. L.; Isenhour, T. L. Minimal Spanning Tree Clustering of Gas Chromatographic Liquid Phases. Comput. Chem. 1977, 1, 145-153. Everitt, B. Cluster Analysis; Halsted: New York, 1974. Balaban, A. T. Chemical Graphs. XXXIV. Five New Topological Indices for the Branching of Tree-Like Graphs. Theor. Chim. Acra 1979, 53, 355-375. Balaban, A. T.; Motoc, I. Chemical Graphs. XXXVI. Correlati...

In this talk we consider some results and open problems from the Chemical Graph Theory, mainly concerning structural indices/properties. The Atom Bond Connectivity index, also known as ABC index was defined by Estrada [4] with relation to the energy of formation of alkanes. It was quickly recognized that this index reflects important structural properties of graphs in general. The ABC index was...

We prove that a connected graph of diameter at least 4 and of girth 7 or more (in particular, a tree) can be exactly reconstructed from metric balls of radius 2 of all its vertices. On the other hand, there exist graphs of diameter 3 and of girth 6 which are not reconstructible. This new graph theory problem is motivated by reconstruction of chemical compounds. © 2007 Published by Elsevier B.V.

Mathematical descriptors of molecular structure, such as various topological indices, have been widely used in structure-property-activity studies (see [5, 6, 12]). Among the numerous topological indices considered in chemical graph theory, only a few have been found noteworthy in practical application (see [10]). One of these is the connectivity index or Randić index. The Randić index of an or...

The study of topological indices - graph invariants that can be used for describing and predicting physicochemical or pharmacological properties of organic compounds - is currently one of the most active research fields in chemical graph theory. In this paper we study the Schultz index and find a relation with the Wiener index of the armchair polyhex nanotubes TUV C(6)[2p; q]. An exact expressi...

The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.

Let L be the Laplacian matrix of a tree. We present a graph-theoretic interpretation of the cofactors of order 2 of L. From this, we deduce a description for the inverse of the rooted Laplacian, reflecting the geometry of a branch. Defining the thickness of a branch as the Perron root of this matrix, we present a minimaxcharacterization of the characteristic center of the tree based on the thic...