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Entropy 2016, 18(5), 183; doi:10.3390/e18050183

A Conjecture Regarding the Extremal Values of Graph Entropy Based on Degree Powers

1
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
2
Department of Biomedical Computer Science and Mechatronics, University for Health Sciences, Medical Informatics and Technology (UMIT), Eduard Wallnoefer Zentrum, A-6060 Hall in Tyrol, Austria
*
Author to whom correspondence should be addressed.
Academic Editor: Andreas Holzinger
Received: 14 March 2016 / Revised: 10 May 2016 / Accepted: 10 May 2016 / Published: 13 May 2016
View Full-Text   |   Download PDF [700 KB, uploaded 13 May 2016]

Abstract

Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. The starting point has been always based on assigning a probability distribution to a network when using Shannon’s entropy. In particular, Cao et al. (2014 and 2015) defined special graph entropy measures which are based on degrees powers. In this paper, we obtain some lower and upper bounds for these measures and characterize extremal graphs. Moreover we resolve one part of a conjecture stated by Cao et al. View Full-Text
Keywords: graphs; information theory; entropy; graph entropy; degree sequences; degree powers graphs; information theory; entropy; graph entropy; degree sequences; degree powers
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Das, K.C.; Dehmer, M. A Conjecture Regarding the Extremal Values of Graph Entropy Based on Degree Powers. Entropy 2016, 18, 183.

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