let g be a simple graph with vertex set v(g) {v1,v2 ,...vn} . for every vertex i v , ( ) i  vrepresents the degree of vertex i v . the h-th order of randić index, h r is defined as the sumof terms1 2 11( ), ( )... ( ) i i ih  v  v  vover all paths of length h contained (as sub graphs) in g . inthis paper , some bounds for higher randić index and a method for computing the higherrandic ind...

Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i  v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih  v  v  v  over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher R...

The general Randić index Rα(G) of a (chemical) graph G, is defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α an arbitrary real number, which is called the Randić index or connectivity index (or branching index) for α = −1/2 proposed by Milan Randić in 1975. The paper outlines the results known for the (general) Randić inde...

Here, we find the characteristics polynomial of normalized Laplacian of a tree. The coefficients of this polynomial are expressed by the higher order general Randić indices for matching, whose values depend on the structure of the tree. We also find the expression of these indices for starlike tree and a double-starlike tree, Hm(p, q). Moreover, we show that two cospectral Hm(p, q) of the same ...

The modified Randić index of a graph G is a graph invariant closely related to the classical Randić index, defined as

Here we study the normalized Laplacian characteristics polynomial (L-polynomial) for trees and specifically for starlike trees. We describe how the L-polynomial of a tree depends on some topological indices. For which, we also define the higher order general Randić indices for matching and which are different from higher order connectivity indices. Finally we provide the multiplicity of the eig...

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph....

The Randić index R(G) of a graph G is the sum of the weights (d(u)d(v))− 1 2 of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we first present a sharp lower bound on the Randić index of conjugated unicyclic graphs (unicyclic graphs with perfect matching). Also a sharp lower bound on the Randić index of unicyclic graphs is given in terms of the order and given ...

The general Randić index of an organic molecule whose molecular graph is G is defined as the sum of (d(u)d(v))α over all pairs of adjacent vertices of G, where d(u) is the degree of the vertex u in G and α is a real number with α 6= 0. In the paper, we obtained sharp bounds on the general Randić index of the Nordhaus-Gaddum type for trees. Also we show that the general Randić index of the Nordh...

The Randić index R(G) of an organic molecule whose molecular graph is G is the sum of the weights (dudv)− 1 2 of all edges uv of G, where du(or dv) denote the degree of vertex u(or v). Efficient formulas for calculating the Randić index of polyomino chains are provided. Mathematics Subject Classification: 05C50, 05C12, 05C05