TY - JOUR
T1 - Entropy bounds for dendrimers
AU - Chen, Zengqiang
AU - Dehmer, Matthias
AU - Emmert-Streib, Frank
AU - Shi, Yongtang
PY - 2014/9/1
Y1 - 2014/9/1
N2 - Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. When considering Shannon entropy-based graph measures, there has been very little work to find their extremal values. A reason for this might be the fact that Shannon's entropy represents a multivariate function and all probability values are not equal to zero when considering graph entropies. Dehmer and Kraus proved some extremal results for graph entropies which are based on information functionals and express some conjectures generated by numerical simulations to find extremal values of graph entropies. Dehmer and Kraus discussed the extremal values of entropies for dendrimers. In this paper, we continue to study the extremal values of graph entropy for dendrimers, which has most interesting applications in molecular structure networks, and also in the pharmaceutical and biomedical area. Among all dendrimers with n vertices, we obtain the extremal values of graph entropy based on different well-known information functionals. Numerical experiments verifies our results.
AB - Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. When considering Shannon entropy-based graph measures, there has been very little work to find their extremal values. A reason for this might be the fact that Shannon's entropy represents a multivariate function and all probability values are not equal to zero when considering graph entropies. Dehmer and Kraus proved some extremal results for graph entropies which are based on information functionals and express some conjectures generated by numerical simulations to find extremal values of graph entropies. Dehmer and Kraus discussed the extremal values of entropies for dendrimers. In this paper, we continue to study the extremal values of graph entropy for dendrimers, which has most interesting applications in molecular structure networks, and also in the pharmaceutical and biomedical area. Among all dendrimers with n vertices, we obtain the extremal values of graph entropy based on different well-known information functionals. Numerical experiments verifies our results.
KW - Dendrimers
KW - Extremal values
KW - Graph entropy
KW - Information theory
KW - Shannon's entropy
UR - http://www.scopus.com/inward/record.url?scp=84903150191&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2014.05.105
DO - 10.1016/j.amc.2014.05.105
M3 - Article
VL - 242
SP - 462
EP - 472
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
ER -