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The connectivity index

Ming‐Hui Lu, Huiqing Liu, Feng Tian

Open publisher page 7 citations

Abstract

Let G be a simple connected graph of order n. The connectivity index Rα(G) of a graph G is the sum of the weights (d(u)d(v)) α of all edges uv of G, where α is a real number (α � = 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. 1.

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What this paper is about

Let G be a simple connected graph of order n. The connectivity index Rα(G) of a graph G is the sum of the weights (d(u)d(v)) α of all edges uv of G, where α is a real number (α � = 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. 1.

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Available abstract

Let G be a simple connected graph of order n. The connectivity index Rα(G) of a graph G is the sum of the weights (d(u)d(v)) α of all edges uv of G, where α is a real number (α � = 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. 1.

Key concepts: Adjacency matrix, Combinatorics, Mathematics, Laplacian matrix, Connectivity, Graph energy, Degree matrix, Graph

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