On the eigenvalues of general sum-connectivity Laplacian matrix

Deng, Hanyuan, Huang, He and Zhang, Jie (2013) On the eigenvalues of general sum-connectivity Laplacian matrix. Journal of the Operations Research Society of China, 1 (3), 347-358. (doi:10.1007/s40305-013-0022-y).

Record type: Article

Abstract

The connectivity index was introduced by Randić (J. Am. Chem. Soc. 97(23):6609-6615, 1975) and was generalized by Bollobás and Erdös (Ars Comb. 50:225-233, 1998). It studies the branching property of graphs, and has been applied to studying network structures. In this paper we focus on the general sum-connectivity index which is a variant of the connectivity index. We characterize the tight upper and lower bounds of the largest eigenvalue of the general sum-connectivity matrix, as well as its spectral diameter. We show the corresponding extremal graphs. In addition, we show that the general sum-connectivity index is determined by the eigenvalues of the general sum-connectivity Laplacian matrix.

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Published date: 1 September 2013

Additional Information: Funding Information: This work was supported by the Danish National Research Foundation and the National Science Foundation of China (No. 61061130540) for the Sino–Danish Center for the Theory of Interactive Computation and by the Center for Research in Foundations of Electronic Markets (CFEM, supported by the Danish Strategic Research Council), within which this work was performed.

Keywords: Connectivity index, Eigenvalue, Laplacian matrix

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