We develop the idea that the use of ad hoc molecular descriptors in QSAR/QSPR studies is not an optimal solution. Instead, we propose to optimize these descriptors for the specific properties under study. In the case of topological indices (TIs) we propose the use of the generalized topological indices (GTIs), which account for several of the classical TIs in one single graph invariant. GTIs re...

Motivation. The Randiü index is one of the most successful molecular descriptors in structure–property and structure–activity relationships studies. In spite of some attempts to interpret the physical meaning of this index it is still not clear what exactly this index measures in a molecular structure. The finding of the structural interpretation of this topological index will open the doors to...

the degree kirchhoff index of a connected graph $g$ is defined as‎ ‎the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $g$‎. ‎bounds for the degree kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎the special case of regular grap...

Correlation of the octane number (ON) of heptane and octane isomers with various topological indices, Z, w, p, and B, was studied. For single parameter correlation the index B by Balaban and w by Wiener show good results, whereas for two-parameter correlation almost any combination among the above four indices was found to give relatively high r value. Further, by adding the third parameter the...

Muscular dystrophies are part of a group of degenerative diseases of the muscular system, which are characterized by muscle degeneration and structural changes at the neuromuscular junction. The most common form is Duchenne Muscular Dystrophy (DMD) (Whitehead et al., 2006), which affects approximately 1 in every 3500 live births (Balaban et al., 2005; Judge et al., 2005; Withehead et al., 2006;...

Among the vast number of polyhex graphs corresponding to polycyclic aromatic hydrocarbons several graphs are known to have a vexing property with respect to the perfect matching, or Kekulć structure counting problem." Examples are 12 and 23, which have the same number of starred I_I and unstarred IO I atoms but have no Kekule structure (See the left half of Figure 1). Further, both of them have...

Let $G=(V,E)$, $V={v_1,v_2,ldots,v_n}$, be a simple graph with$n$ vertices, $m$ edges and a sequence of vertex degrees$Delta=d_1ge d_2ge cdots ge d_n=delta$, $d_i=d(v_i)$. Ifvertices $v_i$ and $v_j$ are adjacent in $G$, it is denoted as $isim j$, otherwise, we write $insim j$. The first Zagreb index isvertex-degree-based graph invariant defined as$M_1(G)=sum_{i=1}^nd_i^2$, whereas the first Zag...

Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new algorithm for computing the detour index of molecular graphs is presented. We apply our algorithm on copper and silver nanoclusters ...