Hosoya and Wiener Index of Zero-Divisor Graph of Z pm q2

Main Article Content

Nazar H. Shuker
Husam Q. Mohammad
Luma A. Khaleel


zero-divisor graph, Clique number , Hosoya polynomial, Wiener index


In this work, we study zero-divisor graph of the ring Zpmq2 and give some properties of this graph. Furthermore we find Hosoya polynomial and Wiener index for this graph.

Abstract 28 | PDF Downloads 34


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.
D. F. Anderson and A. Badawi, The zero-divisor graph of a commutative semigroup, a survey. In Groups, modules, and model theory-surveys and recent developments, Springer, Cham, (2017), pp23–39.
D. F. Anderson and P. Livindston, The Zero-divisor graph of a commutative ring, Journal of Algebra, 217, (1999) ,pp434-447.
M.F. Atiyah, I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Pub- lishing Company, (1969).
M ,Axtell ,J. Stickles ,W .Trampbachls ,Zero-divisor ideal and realizable Zero- divisor graph,2(1),(2009),pp17-27.
F. Buckley and F. Harary , Distance in Graphs. Addison -Wesley , New York, (1990).
A. Duane, "Proper coloring and p-partite structures of the zero divisor
graph" Rose Hulman Undergraduate Math Journal 7, 2006.
I.Gutman ; Some properties of the Wiener polynomial ; Graph Theory Notes of New York; XXV .The New York Academy of Sciences 13-17, (1993).
H.Hosoya;'On some counting polynomial in chemistry ',Discrete Applied Math. Vol.19,239-257,(1985)
H.Q. Mohammad and M. N. Authman, "Hosoya polynomial and Wiener index of zero-divisor graph of Zn," Al-Rafidain Journal of computer scinces and mathematics., 2018.
N. H. Shuker and H. Q. Mohammad, " The Zero Divisor Graphs of a finite Certain Rings ", The 6th Scientific Conference of the College of Computer Sciences & Mathematics, Iraqi Journal of Statistical Sciences Vol.25, 2013, pp.14.

J. T. Wang, "Zero Divisor of Commutative Rings", M.Sc. Thesis theUniversity of National Chung Cheng , Taiwan,2005

H. Wiener, "Structural determination of paraffin boiling points", Journal of the American Chemical Society, vol. 69, pp. 17-20, 1947.