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结构-性质建模中基于度的图熵

Degree-Based Graph Entropy in Structure-Property Modeling.

作者信息

Mondal Sourav, Das Kinkar Chandra

机构信息

Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea.

Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur 603203, Tamil Nadu, India.

出版信息

Entropy (Basel). 2023 Jul 21;25(7):1092. doi: 10.3390/e25071092.

DOI:10.3390/e25071092
PMID:37510039
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10379043/
Abstract

Graph entropy plays an essential role in interpreting the structural information and complexity measure of a network. Let be a graph of order . Suppose dG(vi) is degree of the vertex vi for each i=1,2,…,n. Now, the -th degree-based graph entropy for is defined as Id,k(G)=-∑i=1ndG(vi)k∑j=1ndG(vj)klogdG(vi)k∑j=1ndG(vj)k, where is real number. The first-degree-based entropy is generated for k=1, which has been well nurtured in last few years. As ∑j=1ndG(vj)k yields the well-known graph invariant first Zagreb index, the Id,k for k=2 is worthy of investigation. We call this graph entropy as the second-degree-based entropy. The present work aims to investigate the role of Id,2 in structure property modeling of molecules.

摘要

图熵在解释网络的结构信息和复杂性度量方面起着至关重要的作用。设 是一个阶数为 的图。假设对于每个 i = 1, 2, …, n，dG(vi) 是顶点 vi 的度。现在，对于 的第 个基于度的图熵定义为 Id,k(G)= -∑i=1ndG(vi)k∑j=1ndG(vj)klogdG(vi)k∑j=1ndG(vj)k，其中 是实数。当 k = 1 时产生基于一阶的熵，在过去几年中它得到了充分的研究。由于 ∑j=1ndG(vj)k 产生了著名的图不变量第一 Zagreb 指数，所以 k = 2 时的 Id,k 值得研究。我们将这种图熵称为基于二阶的熵。本工作旨在研究 Id,2 在分子结构性质建模中的作用。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/417e46d0fb14/entropy-25-01092-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/8d00e1109c0c/entropy-25-01092-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/92f849c34418/entropy-25-01092-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/e9da84f3e4b5/entropy-25-01092-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/c989456454e7/entropy-25-01092-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/ecd002869479/entropy-25-01092-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/8725e6282cee/entropy-25-01092-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/53764890f65d/entropy-25-01092-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/417e46d0fb14/entropy-25-01092-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/8d00e1109c0c/entropy-25-01092-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/92f849c34418/entropy-25-01092-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/e9da84f3e4b5/entropy-25-01092-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/c989456454e7/entropy-25-01092-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/ecd002869479/entropy-25-01092-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/8725e6282cee/entropy-25-01092-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/53764890f65d/entropy-25-01092-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/71b2/10379043/417e46d0fb14/entropy-25-01092-g008.jpg

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