An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...

Kim A. Eagle, MD; Geoffrey S. Ginsburg, MD, PhD; Kiran Musunuru, MD, PhD, MPH; William C. Aird, MD; Robert S. Balaban, PhD; Susan K. Bennett, MD; Roger S. Blumenthal, MD; Shaun R. Coughlin, MD, PhD; Karina W. Davidson, PhD; Edward D. Frohlich, MD; Philip Greenland, MD; Gail P. Jarvik, MD, PhD; Peter Libby, MD; Carl J. Pepine, MD; Jeremy N. Ruskin, MD; Arthur E. Stillman, MD, PhD; Jennifer E. Va...

Symmetry properties of the three 10-cages on 70 vertices are investigated. Being bipartite, these graphs are Levi graphs of triangleand quadrangle-free (353) con!gurations. For each of these graphs a Hamilton cycle is given via the associated LCF notation. Furthermore, the automorphism groups of respective orders 80, 120, and 24 are computed. A special emphasis is given to the Balaban 10-cage, ...

Abstract. Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. A graph is a ...

Kim A. Eagle, MD; Geoffrey S. Ginsburg, MD, PhD; Kiran Musunuru, MD, PhD, MPH; William C. Aird, MD; Robert S. Balaban, PhD; Susan K. Bennett, MD; Roger S. Blumenthal, MD; Shaun R. Coughlin, MD, PhD; Karina W. Davidson, PhD; Edward D. Frohlich, MD; Philip Greenland, MD; Gail P. Jarvik, MD, PhD; Peter Libby, MD; Carl J. Pepine, MD; Jeremy N. Ruskin, MD; Arthur E. Stillman, MD, PhD; Jennifer E. Va...

We present an application of the chemical graph theory approach for generating elementary reactions of complex systems. Molecular species are naturally represented by graphs, which are identified by their vertices and edges where vertices are atom types and edges are bonds. The mechanism is generated using a set of reaction patterns (sub-graphs). These subgraphs are the internal representations...

Recently, a new molecular graph matrix, Harary matrix, was defined in honor of Professor Frank Harary, and new graph invariants (local and global) based on it were also defined and researched, Harary index is one of these invariants. The Harary matrix can be used to derive a variant of the Balaban index, Harary index was also successfully tested in several structure-property relationships, so i...

A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of ...