Degree Distance of Zero-Divisor Graph Г[Z_n ]

Year 2020, Volume: 24 Issue: 3, 531 - 535, 01.06.2020

N.feyza Yalçın

https://doi.org/10.16984/saufenbilder.549532

Abstract

In this article, degree distance of zero-divisor graph Г[Z_n ] is computed for n=p^2,n=pq and n=p^3, where p,q are distinct prime numbers.

Keywords

Zero-divisor graph, degree distance, topological index, graph

References

• [1] M.R., Ahmadi and R., Jahani-Nezhad, “Energy and Wiener index of zero divisor graphs”, Iranian Journal of Mathematical Chemistry, vol. 2, pp. 45-51, 2011.
• [2] D.F., Anderson and P.S., Livingston, “The zero-divisor graph of a commutative ring”, Journal of Algebra, vol. 217, pp. 434-447, 1999.
• [3] I., Beck, “Coloring of commutative rings”, Journal of Algebra, vol. 116, no.1,pp. 208-226, 1988.
• [4] A.A., Dobrynin and A.A., Kochetova, “Degree Distance of a Graph: A Degree analogue of the Wiener Index”, Journal of Chemical Information and Computer Sciences, vol. 34, pp. 1082-1086, 1994.
• [5] I., Gutman, “Selected properties of the Schultz molecular topological index”, Journal of Chemical Information and Computer Sciences, vol. 34, pp. 1087-1089, 1994.
• [6] W., Imrich and S., Klavzar, “Product Graphs: Structure and Recognition”, John Wiley&Sons, New York, USA, 2000.
• [7] M.H., Khalifeh, H., Yousefi-Azari and A.R., Ashrafi, “The Hyper-Wiener index of graph operations”, Comput. Math. Appl., vol. 56, pp. 1402-1407, 2008.
• [8] H.Q., Mohammad and M.N., Authman, “Hosoya polynomial and Wiener index of zero-divisor graph of Z_n”, Raf. J. Comp.&Math's., vol. 12, no. 1, pp. 47-59, 2018.
• [9] B.S., Reddy, R.S., Jain, N., Laxmikanth, “Eigenvalues and Wiener index of the zero divisor graph Г[Z_n ]”, https://arxiv.org/pdf/1707.05083, 2017.
• [10] H., Wiener, “Structural determination of paraffin boiling points”, Journal of the American Chemical Society, vol. 69, pp. 17-20, 1947.