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For a graph, the first Zagreb index M 1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M 2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. This paper investigates the Zagreb indices of unicyclic graphs by introducing some transformations, and characterize the unicyclic graphs… (More)

- Shubo Chen, Weijun Liu
- 2012

For a graph G = (V, E), the modified Schultz index of G is defined as S * (G) = {u,v}⊆V (G) where d G (u) (or d(u)) is the degree of the vertex u of G, and d G (u, v) is the distance between u and v. Let B(n) be the set of bicyclic graph with n vertices. In this paper, we study the modified Schultz index of B(n), graphs in B(n) with the smallest modified… (More)

If G is a (molecular) graph with n vertices, and d i is the degree of its i-th vertex, then the sum-connectivity index of G is the sum of the weights (d u + d v) − 1 2 of all edges uv of G. A polyomino system is a finite 2-connected plane graph such that each interior face (or say a cell) is surrounded by a regular square of length one. Formulas for… (More)

The Randi´c index R(G) of an organic molecule whose molecular graph is G is the sum of the weights (d u d v) − 1 2 of all edges uv of G, where d u (or d v) denote the degree of vertex u(or v). Efficient formulas for calculating the Randi´c index of polyomino chains are provided.

For a graph, the first Zagreb index M 1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M 2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Denote by G n,k the set of graphs with n vertices and k cut edges. In this paper, we showed the types of graphs with the largest and the… (More)