TY - JOUR

T1 - Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring

T2 - A Polynomial Approach

AU - Mondal, Sourav

AU - Imran, Muhammad

AU - De, Nilanjan

AU - Pal, Anita

N1 - Publisher Copyright:
© 2023 Sourav Mondal et al.

PY - 2023

Y1 - 2023

N2 - The algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices. The topological index is utilized as a significant tool in the study of the quantitative structure activity relationship (QSAR) and quantitative structures property relationship (QSPR) which correlate a molecular structure to its different properties and activities. Graphs containing finite commutative rings have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this article, the topological indices of the total graph Tℤnn∈ℤ+, the zero divisor graph Γℤrn (r is prime, n∈ℤ+), and the zero divisor graph Γℤr×ℤs×ℤt (r,s,t are primes) are computed using some algebraic polynomials.

AB - The algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices. The topological index is utilized as a significant tool in the study of the quantitative structure activity relationship (QSAR) and quantitative structures property relationship (QSPR) which correlate a molecular structure to its different properties and activities. Graphs containing finite commutative rings have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this article, the topological indices of the total graph Tℤnn∈ℤ+, the zero divisor graph Γℤrn (r is prime, n∈ℤ+), and the zero divisor graph Γℤr×ℤs×ℤt (r,s,t are primes) are computed using some algebraic polynomials.

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U2 - 10.1155/2023/6815657

DO - 10.1155/2023/6815657

M3 - Article

AN - SCOPUS:85151521996

SN - 1076-2787

VL - 2023

JO - Complexity

JF - Complexity

M1 - 6815657

ER -