let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...

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, ...

In this paper, we examine the uniqueness (discrimination power) of a newly proposed graph invariant based on the matrix DMAX defined by Randić et al. In order to do so, we use exhaustively generated graphs instead of special graph classes such as trees only. Using these graph classes allow us to generalize the findings towards complex networks as they usually do not possess any structural const...

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 ...

Let $G=(V,E)$ be a simple connectedgraph with $n$ vertices, $m$ edges and sequence of vertex degrees$d_1 ge d_2 ge cdots ge d_n>0$, $d_i=d(v_i)$, where $v_iin V$. With $isim j$ we denote adjacency ofvertices $v_i$ and $v_j$. The generalsum--connectivity index of graph is defined as $chi_{alpha}(G)=sum_{isim j}(d_i+d_j)^{alpha}$, where $alpha$ is an arbitrary real<b...