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

Degree-Based Graph Entropy in Structure-Property Modeling

Sourav Mondal  1   2 , Kinkar Chandra Das  1
Affiliations

Degree-Based Graph Entropy in Structure-Property Modeling

Sourav Mondal et al. Entropy (Basel). .

Abstract

Graph entropy plays an essential role in interpreting the structural information and complexity measure of a network. Let G be a graph of order n. Suppose dG(vi) is degree of the vertex vi for each i=1,2,…,n. Now, the k-th degree-based graph entropy for G is defined as Id,k(G)=-∑i=1ndG(vi)k∑j=1ndG(vj)klogdG(vi)k∑j=1ndG(vj)k, where k 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.

Keywords: QSPR analysis; chemical graph theory; entropy; molecular graph; topological index.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Molecular graph representations of octanes.
Figure 2
Figure 2
Linear fitting of Id,2 with entropy and HVAP for octanes.
Figure 3
Figure 3
Linear fitting of Id,2 with DHVAP and AF for octanes.
Figure 4
Figure 4
Experimental vs. predicted AF and residual plot.
Figure 5
Figure 5
Molecular graphs of benzenoid hydrocarbons.
Figure 6
Figure 6
Linear fitting of Id,2 with Eπ and BP for benzenoid hydrocarbons.
Figure 7
Figure 7
Molecular graphs of some chemicals useful in drug preparation.
Figure 8
Figure 8
Linear fitting of Id,2 with BP and MR for some structures displayed in Figure 7.
See this image and copyright information in PMC

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