TY - JOUR

T1 - Algebraic Structure Graphs over the Commutative Ring Zm

T2 - Exploring Topological Indices and Entropies Using M-Polynomials

AU - Alali, Amal S.

AU - Ali, Shahbaz

AU - Hassan, Noor

AU - Mahnashi, Ali M.

AU - Shang, Yilun

AU - Assiry, Abdullah

N1 - Funding information: This article is supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R231), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

PY - 2023/9/7

Y1 - 2023/9/7

N2 - 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.

AB - 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.

KW - algebraic graph theory

KW - algebraic structure graph

KW - commutative ring

KW - zero-divisor graphs

KW - M-polynomials

KW - Zagreb group indices

UR - http://www.scopus.com/inward/record.url?scp=85176469542&partnerID=8YFLogxK

U2 - 10.3390/math11183833

DO - 10.3390/math11183833

M3 - Article

SN - 2227-7390

VL - 11

JO - Mathematics

JF - Mathematics

IS - 18

M1 - 3833

ER -