Aug 2026· Discrete Mathematics, Algorithms and Applications (DMAA)· 0 citations
Abstract
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.
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, E. Güner· Eskişehir Teknik Üniversites...· 0 citations
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.
Seda Oğuz Ünal· Balıkesir Üniversitesi Fen B...· 0 citations
Consider a group [Formula: see text] and construct its power graph, whose vertex set consists of the elements of [Formula: see text]. Two distinct vertices (elements) are adjacent in the graph if and only if one element can be expressed as an integral power of the other. In this article, we improved the bounds of the spectral radius of the power graphs of the cyclic group [Formula: see text], the dihedral group [Formula: see text], and the dicyclic group [Formula: see text]. For [Formula: see text] the power graph of the cyclic group [Formula: see text] is not a complete multipartite graph. We find the second largest eigenvalue bounds of the same with the clique number. In some cases, we find the bounds are exact if and only if they belong to a particular family of graphs. Lastly, we work on the distance spectral radius of the power graphs of the same groups
Priti Prasanna Mondal, Basit A. Mir, Fouzul Atik· Journal of Algebra and its A...· 0 citations
This study explores the spectral characteristics and energy distributions associated with selected graph operations derived from the first Zagreb, second Zagreb, and sum-connectivity matrices to contribute to understanding how algebraic operations induce spectral energy shifts analogous to perturbations in physical or molecular graph systems.
S. Sripriya, A. Anuradha· Baghdad Science Journal· 0 citations
This paper presents a new graph family called Double Star Double Fanbell (BSDF) which consists of double star graph with each pendant vertex added with a double fan graph, which provides a proper model for the highly branched organic compounds, dendrimer, hyperbranched polymers, and functional nanomaterials.
Babysuganya K, Maheswari M, N. A et al.· Adolescência e Saúde· 0 citations
The singular difference graph, denoted by $\Gamma$, of the vector space of square matrices over a field is a graph whose vertex set is the set of all elements of the vector space, where two distinct vertices are adjacent if and only if the difference of the corresponding matrices is singular. In this paper, we investigate fundamental graph-theoretic properties of $\Gamma$, including connectivity, diameter, regularity, the Eulerian property, independence number, clique number, and domination number. We show that $\Gamma$ is a connected regular graph with diameter two. Over finite fields, we obtain an explicit formula for the degree of each vertex and characterize precisely when $\Gamma$ is Eulerian. We determine the independence number and clique number and provide explicit constructions attaining these values using companion matrices of irreducible polynomials. We also construct an explicit dominating set, yielding an upper bound for the domination number.
Shrinath Hadimani· 0 citations
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