Algebraic Structure Graphs over the Commutative Ring Zm: Exploring Topological Indices and Entropies Using M-Polynomials

Amal S. Alali*, Shahbaz Ali*, Noor Hassan, Ali M. Mahnashi, Yilun Shang, Abdullah Assiry

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
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Abstract

The field of mathematics that studies the relationship between algebraic structures and graphs is known as algebraic graph theory. It incorporates concepts from graph theory, which examines the characteristics and topology of graphs, with those from abstract algebra, which deals with algebraic structures such as groups, rings, and fields. If the vertex set of a graph G^ is fully made up of the zero divisors of the modular ring Zn, the graph is said to be a zero-divisor graph. If the products of two vertices are equal to zero under (modn), they are regarded as neighbors. Entropy, a notion taken from information theory and used in graph theory, measures the degree of uncertainty or unpredictability associated with a graph or its constituent elements. Entropy measurements may be used to calculate the structural complexity and information complexity of graphs. The first, second and second modified Zagrebs, general and inverse general Randics, third and fifth symmetric divisions, harmonic and inverse sum indices, and forgotten topological indices are a few topological indices that are examined in this article for particular families of zero-divisor graphs. A numerical and graphical comparison of computed topological indices over a proposed structure has been studied. Furthermore, different kinds of entropies, such as the first, second, and third redefined Zagreb, are also investigated for a number of families of zero-divisor graphs.
Original languageEnglish
Article number3833
Number of pages25
JournalMathematics
Volume11
Issue number18
DOIs
Publication statusPublished - 7 Sept 2023

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