Jul 2026· Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi· Vol 28, pp. 958-980· 0 citations· 16 references
Abstract
Topological indices play a fundamental role in the study of graph structures and their quantitative properties, particularly in applications related to chemistry, network science, and dynamic system analysis. In this work, we study the Reduced Zagreb index, Zagreb coindices, and the PI index of monogenic semigroup graphs, a well-studied class of algebraic graphs with relevance to both pure and applied mathematics. Using the adjacency structure of the graph as the main tool, we derive exact closed-form expressions for these indices and illustrate the results through explicit examples. Furthermore, we obtain explicit parity-dependent closed-form formulas for the reduced first Zagreb index, reduced second Zagreb index, Zagreb coindices and the vertex-PI index of monogenic semigroup graphs. The derivations are based on a neighbourhood-block decomposition of the edge set, which provides a unified computational framework for several families of degree-based topological indices. These results demonstrate how the algebraic structure of a monogenic semigroup determines the behaviour of important graph-theoretical descriptors.
Wiener-type distance-based topological indices (Wiener, Wiener polarity, hyper-Wiener, Harary, reciprocal complementary Wiener, and terminal Wiener) are discussed and recalculated by considering the odd and even cases of n.
H. Topcu, Eda Güner· Eskişehir Teknik Üniversites...· 0 citations
This study investigates the structure of non-coprime graphs derived from the dihedral groups of prime power order using approaches from graph theory and group theory. In molecular representation and pure mathematics, graphs serve a tool to illustrate the internal structure of systems through topological indices. A non-...
Dimas Indrawadi, I. G. A. W. Wardhana, Hazzirah Izzati Mat Hassim et al.· Jurnal Matematika Statistika...· 0 citations
Topological indices can be used to characterize molecular topology. These are numerical measurements of a suggested molecule’s fundamental structural characteristics, derived from its molecular structure. This numerical value, which is derived from a chemical configuration, represents the important physical properties...
Jayavel Pooja, Venkatesan Muthukumaran, B. Rather et al.· Discrete Mathematics, Algori...· 0 citations
In this paper, we introduce a novel graph structure, namely the subdivision-edge-cycle graph, denoted by SE
1
(X), and derive explicit expressions for the first Zagreb index, second Zagreb index and F-index. The chemical relevance of the proposed graph transformation is demonstrated through QSPR modeling of benzeno...
G. Chetana, B. Bhuvana, M. Shanmukha et al.· Discrete Mathematics, Algori...· 0 citations
The zero-divisor graph of a commutative ring, Γ(R), is a prominent subject in graph theory. Previous research has investigated the energy and topological indices of Γ(ℤₚ[x]/⟨x⁴⟩) for any prime p; however, errors were identified in the characteristic polynomial and the associated energy bounds. Recent work by Rather add...
Vira Hari Krisnawati, Ayunda Faizatul Musyarrofah, Ari Andari· Science and Technology Indon...· 0 citations
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