Exact Distance-Based Topological Indices Of Double Star Double Fanbell Graphs With Applications In Chemical Graph Theory, QSPR/QSAR Modeling, And Drug Discovery

Topological Indices of Chemical Graphs and Their Applications in QSPR and QSAR Modelling

WIENER TYPE TOPOLOGICAL INDICES OF SOME WELL-KNOWN UNICYCLIC GRAPHS

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.

Degree and Distance-based topological indices of power graphs of finite non-abelian groups

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 of the proposed molecule. We use an algebraic number to connect the chemical composition with various physical characteristics, biological activity, and chemical reactivity. A graph with a vertex set of [Formula: see text] in which two unique vertices are adjacent when one element is an integral power of the other is called a power graph [Formula: see text] of a finite group [Formula: see text]. This paper investigates several types of topological indices of power graphs for different finite groups based on distance, degree, and independent sets. We compute the Hyper Wiener Index, Degree Distance Index, Additively Weighted Harary Index, Gutman Index, Multiplicatively Weighted Harary Index, Eccentric Connectivity Index, Connective Eccentricity Index, and Merrifield Simmons Index of power graphs for finite cyclic and non-cyclic groups of order [Formula: see text], dihedral and generalized quaternion groups, where [Formula: see text] are distinct primes. As a consequence, we fix the flaws in the results of [5] and present their correct forms.

Degree-based topological indices of monogenic semigroup graphs: reduced Zagreb indices, coindices and PI index

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.

Closed-form connection-number-based topological indices for porphyrazine and tetrakis-porphyrazine networks.

Graph theory offers a mathematical foundation for modeling and analyzing complicated chemical structures and reaction systems. Topological indices are fundamental tools for measuring structural characteristics and predicting physicochemical and biological properties, with broad applications in chemistry, biology, environmental toxicology, and drug discovery. This study focuses on the two molecular graph families, porphyrazine and tetrakis porphyrazine, which contain complex ring structures. For each graph family, we determine the edge partition induced by endpoint connection numbers and use it to derive closed-form expressions for the general Randić connection index, the first and second Zagreb connection indices and coindices, the atom-bond connectivity connection index, the hyper-Zagreb connection index, the geometric-arithmetic connection index, the forgotten connection index, the augmented Zagreb connection index, and three redefined Zagreb connection indices. The dependence of each formula on the graph parameter n is examined in the graphical comparison section. This analysis enables a direct comparison of the growth trends and structural variations of the two graph families.

Bounds on Product Version of Distance-Related Topological Indices of Complement of Mycielskian Graph

Eccentricity-based topological indices are valuable descriptors for analyzing molecular graphs and complex networks. This paper focuses on the complement of the Mycielskian graph of a connected graph. We derive new upper bounds for several recently introduced eccentricity-related topological indices by exploiting the structural characteristics of the complement graph. The obtained inequalities improve the theoretical understanding of these descriptors and provide efficient estimates for transformed graphs. The proposed results offer new insights into complement graph theory and support further applications in chemical graph theory and related fields.