Mathematical and chemical properties of geometry-based invariants and its applications

Liu, Hechao

doi:10.1016/j.molstruc.2023.136060

Cited by 4 publications

(4 citation statements)

References 17 publications

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“…Graph invariants of the form (1) are being investigated for half a century (since 1970s), but only quite recently it was recognized that the vertex-degree pairs ðd u , d v Þ can be viewed as a point in a two-dimensional coordinate system [9]. This observation made it possible to gain a geometric interpretation of several earlier existing topological indices, and resulted in the design of some new [8,10,11].…”

Section: Introductionmentioning

confidence: 99%

Geometric approach to vertex‐degree‐based topological indices–Elliptic Sombor index, theory and application

Gutman,

Furtula,

2024

Int J of Quantum Chemistry

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A novel geometric method is proposed for constructing vertex‐degree‐based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices. This approach enables a geometric interpretation of several previously known topological indices, and lead to design of a few new. The area of the ellipse induces a vertex‐degree‐based topological index of remarkable simplicity, which we call elliptic Sombor index(). The main mathematical properties of are established, especially its relations to other, earlier known, indices. Then the applicative potential of is analyzed.

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Section: Introductionmentioning

confidence: 99%

Geometric approach to vertex‐degree‐based topological indices–Elliptic Sombor index, theory and application

Gutman,

Furtula,

2024

Int J of Quantum Chemistry

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“…A few years ago, it was discovered that some of these graph invariants have a geometric interpretation (Gutman, 2021). Eventually, this triggered a whole series of geometry-based research studies on VDB invariants (Ali et al, 2024;Gutman, 2022;Gutman et al, 2024;Imran et al, 2022;Liu, 2023b;Tang et al, 2024). The first geometry-motivated VDB invariant is the Sombor index (Gutman, 2021), defined as…”

Section: Introductionmentioning

confidence: 99%

“…Although relatively new, the Sombor index has been a subject of numerous mathematical studies; see the review (Liu et al, 2022), the most recent papers (Attarzadeh & Behtoei, 2024;Chen & Zhu, 2024;Selenge & Horoldagva, 2024;Shetty & Bhat, 2024), and the references cited therein. The Sombor index found also noteworthy applications, especially in chemistry (Hayat et al, 2024;Rauf & Ahmad, 2024;Redžepović, 2021).…”

Section: Introductionmentioning

confidence: 99%

Relating Sombor and Euler indices

Gutman

2024

Vojnotehnički glasnik

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Introduction/purpose: The Euler-Sombor index (EU) is a new vertexdegree-based graph invariant, obtained by geometric consideration. It is closely related to the Sombor index (SO). The actual form of this relation is established. Methods: Combinatorial graph theory is applied. Results: The inequalities between EU and SO are established. Conclusion: The paper contributes to the theory of Sombor-index-like graph invariants.

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“…He et al [24] explored the extremal values of revised Szeged index of unicyclic graphs with given diameter and minimum edge. For more extremal results related to unicyclic graph, see [25], [26], [27], [28].…”

Section: Introductionmentioning

confidence: 99%

Extremal Gourava indices of unicyclic graphs

Yuxin,

Zhou,

Qifan

2023

Preprint

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Topological indices are useful molecular descriptors to measure Quantitative Structure-Activity Relationship (QSAR), Quantitative Structure-Property Relationship (QSPR) and Quantitative Structure-Toxicity Relationship (QSTR). Recently, some novel topological indices of graphs, called the first Gourava index ($CO_1$) and the second Gourava index ($CO_2$), have been proposed to characterize the nature of chemical compounds or interconnection networks. The first and the second Gourava indices of the graph $G$ are denoted by $C{O_1}(G) =\sum\limits_{uv \in E(G)} {[{d_u}} + {d_v} + {d_u}{d_v}]$ and $C{O_2}(G) = \sum\limits_{uv \in E(G)} {[({d_u}} + {d_v}){d_u}{d_v}]$, where $d_u$ is the degree of vertex $u$. In this work, we investigate the extremal values on the first and the second Gourava indices of $n$-vertex unicyclic graphs and characterize the unicyclic graphs that achieve the extremes. We show that, for $n$-vertex unicyclic graph $G$, $8n \le C{O_1}(G) \le 2{n^2} - n + 9$ and $16n \le C{O_2}(G) \le n^3 +3n + 12$, where the lower bound is achieved by $C_n$ and the upper bound is achieved by $G_{3,1}^{(n)}$, which is obtained by attaching $n- 3$ leaves to one vertex of $C_3$. Furthermore, we investigate the applications of Gourava indices to the benzenoid hydrocarbons and show that they can predict the physico-chemical properties of molecules precisely.

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Mathematical and chemical properties of geometry-based invariants and its applications

Cited by 4 publications

References 17 publications

Geometric approach to vertex‐degree‐based topological indices–Elliptic Sombor index, theory and application

Geometric approach to vertex‐degree‐based topological indices–Elliptic Sombor index, theory and application

Relating Sombor and Euler indices

Extremal Gourava indices of unicyclic graphs

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