Energy and Wiener index of divisor graph of commutative ring
P. D. Khandarekhandareprakash789@gmail.comDepartment of Mathematics and StatisticsGES’s Shri Bhausaheb Vartak CollegeBorivali, Maharashtra, 400091, IndiaView full profile → , Suryakant M Jogdandsmjog12@gmail.comDepartment of MathematicsSSGM College, LohaNanded, Maharashtra, 431708, IndiaView full profile → , *R.A. MUNESHWARCorresponding authormuneshwarrajesh10@gmail.comDepartment of MathematicsNES’s Science CollegeNanded, Maharashtra, 131602, IndiaView full profile →
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- Received:
- 03 Mar 2022
- Accepted:
- 10 Aug 2022
- Published Online:
- 10 Oct 2023
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1287
- Pages:
- 957–974
Abstract
Keywords
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References
[1] Anderson. D. F and Livingston P. S: The zero-divisor graph of a commutative ring, Journal of Algebra, 217 (1999), 434-447.
[2] Beck. I, Colouring of a commutative ring, J. Algebra 116 (1988) 208–226.
[3] F. Zhang : The Schur Complement and its application, Springer(2005).
[4] I Gutman : The energy of a graph, Ber. Math-Stat. Sekt. Forschungszent Graz,10(1978)1-22.
[5] I Gutman : The energy of graph: old and new result, Algebraic Combinatorics and Applications, Springer-verlag. Berlin(2001),196-211.
[6] Mohammad Reza Ahmadi and Reza Jahani-Nezhad: Energy and Weiner Index of Zero divisor graphs, Iranian Journal of Mathematical Chemistry, 2(1), (2011), 45-51.
[7] P. M. Magi, SR. Maghe Joshe, Anjaly Kishore: Adjacency Matrix and Eigen Value of the Zero Divisor Graph, J. Math. Comput. Sci. 10 (2020), No. 4, 1285-1297.
[8] Philip D. Powell: Calculating Determinants of Block Matrices, arXiv:1112.4379v1, (2011).
[9] P. D. Khandare, S. M. Jogdand, R. A. Muneshwar: On the Divisor Graph of Finite Commutative Ring, J. Math. Comput. Sci.,12:169(2022).
[10] S.Akbari, A.Mohammadian: On the Zero divisor graph of a commutative rings, J.Algebra, 274, 847-855 (2004).
[11] S. Reddy, R.S. Jain, N. Laxmikanth : Eigenvalues and Wiener index of the zero-divisor graph arXiv preprint arXiv:1707.05083(2017).
[12] Sarfraz Ahmad, Hafiz Muhammad Afzal Siddiqui, Arfan Ali, Mohammad R., Farahani, Muhammad Imran and Ismail Naci Cangul: On Wiener index and Wiener polarity index of some polyomino chains, Journal of Discrete Mathematical Sciences and Cryptography, 22:7, 1151-1164(2019).
[13] Sandeep S Joshi, Kishor F. Pawar: Energy, Weiner Index and Line Graph of prime Graph of Ring, International Journal of Math. Combin. Volume 3(2018), 74-80.
[14] West. D. B: Introduction to Graph Theory, Prentice Hall, 2001.




