Main Article Content
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.
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.