The present note is devoted to establish some extremal results for the zeroth-order general Randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

the first extended zeroth-order connectivity index of a graph   g is defined as 0 1/2 1 ( ) ( ) ,   v   v v g      g d      where   v   (g) is the vertex set of g, and v d is the sum of degrees of neighbors of vertex v in g. we give a sharp lower bound for the first extended zeroth-order connectivity index of trees with given numbers of vertices and pendant vertices,...

Recently, the subdivision Randic index was introduced. In this paper, we present new version of Randic index by using some graph operator and in related to the subdivision Randic index. Next, by using some results about this version, it is computed for TUC C (R) nanotubes. 4 8

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 present note is devoted to establish some extremal results for the zerothorder general Randić index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.