The connectivity index of a weighted graph Original Research Article

Let G be a simple graph and consider the m-connectivity index image , where i1 − i2 −rightwards wave arrow−im+1 runs over all paths of length m in G and di denotes the degree of the vertex i. We find upper bounds for mξ(G) using the eigenvalues of the Laplacian matrix of an associated weighted graph. The method provides also lower bounds for 1ξ(G).