On the basic properties of the compressed annihilator graph of Zn

Document Type : Research Paper

Authors

1 Department of Mathematics, Manonmaniam Sundaranar University Tirunelveli 627 012, Tamil Nadu, India.

2 Department of Mathematics, Gobi Arts and Science College Karattadipalayam Gobichettipalayam-638 453, Tamil Nadu, India

Abstract

For a commutative ring R, the compressed annihilator graph AGE(R) is defined by, taking the equivalence classes of zero divisors of R as the vertex set and two distinct vertices [a] and [b] are adjacent if and only if ann(a)∪ann(b)⊂ann(ab). In this paper, we discuss some of the basic properties such as degree of the vertices, Eulerian, regularity, domination number and planarity of AGE(Zn), where Zn is the ring of integer modulo n.

Keywords

References

[1] S. Alikhani and Y.H. Peng, Introduction to domination polynomial of a graph, Ars Combin. 114 (2014) 257-266.
[2] D. F. Anderson and J. D. LaGrange, Commutative Boolean Monoids, reduced rings and the compressed zero-divisor graphs, J. Pure and Appl. Algebra, 216 (2012) 1626-1636
[3] I. Beck, Coloring of commutative rings, J. Algebra, 116 (1988) 208-226.
[4] B. Mohar and C. Thomassen, Graphs on Surfaces, The Johns Hopkins University Press, Baltimore and London, 1956.
[5] J. A. Bondy and U. S. R. Murty, Graph Theory and its Applications, American Elsevier, New York, 1976.
[6] D. S. Dummit and R. M. Foote, Abstract Algebra, Second edition, Wiley Student edition, New Jersey, 2008.
[7] M. M. Syslo, Characterizations of Outer planar graphs, Discrete Math., 26 No. 1 (1979) 47-53.
[8] S. Payrovi and S. Babaei, The compressed annihilator graph of a commutative ring, Indian J. Pure Appl. Math., 49 No. 1 (2018) 177-186
Algebraic Structures and Their Applications
Volume 10, Issue 1
February 2023
Pages 131-139

Files

Share

How to cite

Statistics