On the Eigenvalues of General Sum-Connectivity Laplacian Matrix

Hanyuan Deng; He Huang; Jie Zhang

doi:10.1007/s40305-013-0022-y

On the Eigenvalues of General Sum-Connectivity Laplacian Matrix

Hanyuan Deng, He Huang, Jie Zhang

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

3 Citations (SciVal)

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.

Original language	English
Pages (from-to)	347-358
Number of pages	12
Journal	Journal of the Operations Research Society of China
Volume	1
Issue number	3
DOIs	https://doi.org/10.1007/s40305-013-0022-y
Publication status	Published - 1 Sep 2013

Keywords

Connectivity index
Eigenvalue
Laplacian matrix

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10.1007/s40305-013-0022-y

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title = "On the Eigenvalues of General Sum-Connectivity Laplacian Matrix",

abstract = "The connectivity index was introduced by Randi{\'c} (J. Am. Chem. Soc. 97(23):6609-6615, 1975) and was generalized by Bollob{\'a}s and Erd{\"o}s (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.",

keywords = "Connectivity index, Eigenvalue, Laplacian matrix",

author = "Hanyuan Deng and He Huang and Jie Zhang",

note = "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.",

year = "2013",

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doi = "10.1007/s40305-013-0022-y",

language = "English",

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T1 - On the Eigenvalues of General Sum-Connectivity Laplacian Matrix

AU - Deng, Hanyuan

AU - Huang, He

AU - Zhang, Jie

N1 - 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.

PY - 2013/9/1

Y1 - 2013/9/1

N2 - 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.

AB - 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.

KW - Connectivity index

KW - Eigenvalue

KW - Laplacian matrix

U2 - 10.1007/s40305-013-0022-y

DO - 10.1007/s40305-013-0022-y

M3 - Article

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SP - 347

EP - 358

JO - Journal of the Operations Research Society of China

JF - Journal of the Operations Research Society of China

SN - 2194-668X

IS - 3

ER -

On the Eigenvalues of General Sum-Connectivity Laplacian Matrix

Abstract

Keywords

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