The general Randić index Rα(G) is the sum of the weights (dG(u)dG(v)) over all edges uv of a (molecular) graph G, where α is a real number and dG(u) is the degree of the vertex u of G. In this paper, for any real number α ≤ −1, the minimum general Randić index Rα(T ) among all the conjugated trees (trees with a Kekulé structure) is determined and the corresponding extremal conjugated trees are ...

The zeroth-order general Randic index, 0R?(G), of a connected graph G, is defined as 0 P R?(G) = ni =1 d?i , where di the degree vertex vi G and ? arbitrary real number. We consider linear combinations 0R?(G) form (? + ?)0R??1(G) ?? 0R??2(G) 2a 0R??1(G) a2 0R??2(G), an number, determine their bounds. As corollaries, various upper lower bounds indices that represent some special cases are obtain...

Let G = (V, E), V {v1, v2,..., vn}, be a simple connected graph of order n and size m, without isolated vertices. Denote by d1 ? d2 ?... dn, di d(vi) sequence vertex degrees G. The general zeroth-order Randic index is defined as 0R?(G) ?ni =1 d?i, where an arbitrary real number. corresponding coindex via 0R??(G) ?ni=1(n?1?di)d?i. Some new bounds for the relationship between 0R??(G?) 0R???1(G?) ...

in this paper an algorithm for computing the balaban and randic indices of any simple connected graph was introduced. also these indices were computed for ipr c80 fullerene isomers, zigzag nanotubes and graphene by gap program.

it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...

it is well known that the chemical behavior of a compound is dependent upon the structure of itsmolecules. quantitative structure – activity relationship (qsar) studies and quantitative structure –property relationship (qspr) studies are active areas of chemical research that focus on the nature ofthis dependency. topological indices are the numerical value associated with chemical constitution...