Degree-Based Topological Indices

By Ivan Gutman. 2013

838 citations recorded by the source corpus.

The degree of a vertex of a molecular graph is the number of first neighbors of this vertex. A large number of molecular-graph-based structure descriptors (topological indices) have been conceived, depending on vertex degrees. We summarize their main properties, and provide a critical comparative study thereof.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/537366b511be3ecb4c3f17f11d90712a31eb2780

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In Computational Theory and Mathematics

In Geometry and Topology

In Organic Chemistry

Citations in the corpus

Multiplicative Zagreb Indices of Molecular Graphs (2019, background): “After this, different impressive TIs are introduced in molecular graph theory [20,21], but the degree-based TIs are famous than others, see [22].”
Vertex-Degree-Based Topological Indices Over Graphs (2014, background): “For recent results on VDB topological indices we refer to ([3],[7],[8],[15]).”
Further Properties of the Second Zagreb Index (2014, background): “Gutman provides an overview of recent developments among degreebased topological indices in [2], while further mathematical properties of M1 and M2 are surveyed in [3, 4].”
The ABC Matrix (2016, methodology): “This has prompted Gutman (2013) to claim that the ABC happens to be the only topological index for which a theoretical, quantum-theory-based, foundation and justi cation has been found.”
An Exceptional Property of First Zagreb Index (2014, background): “For details of their chemical applications and mathematical theory see the surveys [5,6,8,13] and the references cited therein.”
M-Polynomial and Degree-Based Topological Indices (2014, background): “e=uv∈E f(du, dv) , (1) where f = f(x, y) is a function appropriately selected for possible chemical applications [15].”
On Zagreb Indices and Coindices (2015, background): “These topological indices were conceived in the 1970s [13, 15]; for details on their properties and additional references see [4, 9, 10, 12, 14, 21]; for historical details see [11].”
Three New/Old Vertex-Degree-Based Topological Indices (2014, background): “Details of these and other degree–based topological indices can be found in the books [20, 21, 28], surveys [5–7, 19, 34–36], recent review [18], and the references cited therein.”