journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-1966 Double Roman domination number of the zero-divisor graphs of commutative rings Kumar Ravindra Department of Mathematics, Ram Sewak Singh Mahila College Sitamarhi, Babasaheb Bhimrao Ambedkar Bihar University, Muzaffarpur, Bihar, 842001, India Department of Mathematics, Indian Institute of Technology Patna, Patna, Bihar, 801106, India Singh Ashutosh Department of Mathematics, Indian Institute of Technology Patna, Patna, Bihar, 801106, India Prakash Om Department of Mathematics, Indian Institute of Technology Patna, Patna, Bihar, 801106, India 28 3 765 781 20 02 2025

In 2016, Beeler et al. [9] introduced the concept of the double Roman dominating function and the double Roman domination number(DRDN) of a graph. Following the same concept, we extend the study and calculate the double Roman domination number of the zero-divisor graph of a commutative ring N  and its complement graph. Also, we find the DRDN of the total graph of the ring N. 

 Commutative ring Roman domination number Double roman domination number Total graph Zero-divisor graph of a ring access open retracted no