Multiplicative Topological Indices of Linear Functional Graphs over Finite Dimensional Vector Spaces.

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Bibliographic Details
Title:	Multiplicative Topological Indices of Linear Functional Graphs over Finite Dimensional Vector Spaces.
Authors:	Lingan, Vinnarasi¹ vinnilingan10@gmail.com, Gnanaprakasam, Kalaimurugan² kalaimurugan@gmail.com, Manuvelleenas, Vimal¹ vimalleenas@gmail.com
Source:	IAENG International Journal of Computer Science. Sep2025, Vol. 52 Issue 9, p3098-3113. 16p.
Subjects:	Topological graph theory, Vector spaces
Abstract:	In this study, we derive several notable topological indices for linear functional graphs over finite dimensional vector spaces. In particular, we obtain certain novel topological indices, such as the multiplicative degree-based topological indices for Zagreb and Hyper Zagreb. In addition to these, we investigated certain noteworthy geometric arithmetic indices in their generalized forms. Reverse multiplicative indices utilize this idea to analyze the inverse of these products, providing an alternate method for measuring connectedness or other structural features of a graph. Refined indices extend classic topological measurements by taking into an account deeper interactions between degrees or higher-order connections, resulting in a more comprehensive representation of network and graph structure. Revan indices are proposed as an extension of traditional degree-based metrics, offering higher sensitivity to subtle structural differences in network topology and effectively distinguishing non-isomorphic graphs with identical global features. Furthermore, we explore elliptic Sombor indices as a novel variant that captures degree-based structural nuances through elliptic functional transformations, enhancing the analytical resolution of graph invariants. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	In this study, we derive several notable topological indices for linear functional graphs over finite dimensional vector spaces. In particular, we obtain certain novel topological indices, such as the multiplicative degree-based topological indices for Zagreb and Hyper Zagreb. In addition to these, we investigated certain noteworthy geometric arithmetic indices in their generalized forms. Reverse multiplicative indices utilize this idea to analyze the inverse of these products, providing an alternate method for measuring connectedness or other structural features of a graph. Refined indices extend classic topological measurements by taking into an account deeper interactions between degrees or higher-order connections, resulting in a more comprehensive representation of network and graph structure. Revan indices are proposed as an extension of traditional degree-based metrics, offering higher sensitivity to subtle structural differences in network topology and effectively distinguishing non-isomorphic graphs with identical global features. Furthermore, we explore elliptic Sombor indices as a novel variant that captures degree-based structural nuances through elliptic functional transformations, enhancing the analytical resolution of graph invariants. [ABSTRACT FROM AUTHOR]
ISSN:	1819656X