Computing Vertex-Based Eccentric Topological Descriptors of Zero-Divisor Graph Associated with Commutative Rings

摘要

The applications of finite commutative ring are useful substances in robotics and programmed geometric, communication theory, and cryptography. In this paper, we study the vertex-based eccentric topological indices of a zero-divisor graphs of commutative ring<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>ℤ</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow><mml:mi>ℤ</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math>, where<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>p</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>q</mml:mi></mml:math>are primes.