A Conjecture Regarding the Extremal Values of Graph Entropy Based on Degree Powers
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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
Entropy 2016, 18(5), 183; https://doi.org/10.3390/e18050183
Received: 14 March 2016 / Revised: 10 May 2016 / Accepted: 10 May 2016 / Published: 13 May 2016
(This article belongs to the Special Issue Machine Learning and Entropy: Discover Unknown Unknowns in Complex Data Sets)
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.
Keywords:
graphs; information theory; entropy; graph entropy; degree sequences; degree powers