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THE ZAGREB INDICES OF RANDOM GRAPHS

Published online by Cambridge University Press:  28 March 2013

Qunqiang Feng ,
Zhishui Hu  and
Chun Su
Qunqiang Feng
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China E-mail: fengqq@ustc.edu.cn; huzs@ustc.edu.cn; suchun@ustc.edu.cn
Zhishui Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China E-mail: fengqq@ustc.edu.cn; huzs@ustc.edu.cn; suchun@ustc.edu.cn
Chun Su
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China E-mail: fengqq@ustc.edu.cn; huzs@ustc.edu.cn; suchun@ustc.edu.cn
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Abstract

Several limit laws for the Zagreb indices of the classical Erdös–Rényi random graphs are investigated in this paper. We have obtained the necessary and sufficient condition for the asymptotic normality of the two Zagreb indices (suitably normalized), as well as the explicit values for the means and variances of both the indices. Besides, the limiting joint distribution of the numbers of paths of various lengths is also studied under several conditions.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 2 , April 2013 , pp. 247 - 260
Copyright
Copyright © Cambridge University Press 2013

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