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The Connectivity Index

Let G be a simple connected graph of order n. The connectivity index R (G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where is a real number ( 6 0), and d(u) denotes the degree of the vertex u. In this paper, we present some new bounds for the connectivity index of a graph G in terms of the eigenvalues of the Laplacian matrix or adjacency matrix of the graph G, from which we can get some known results.