1 |
S. Akbari and A. Mohammadian, On zero-divisor graph of finite rings, J. Algebra 314 (2007), no. 1, 168-184.
DOI
|
2 |
F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1992.
|
3 |
D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra 159 (1993), no. 2, 500-517.
DOI
|
4 |
D. F. Anderson, R. Levy, and J. Shapiro, Zero-divisor graphs, von Neumann regular rings, and Boolean algebras, J. Pure Appl. Algebra 180 (2003), no. 3, 221-241.
DOI
|
5 |
D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217, (1999), no. 2, 434-447.
DOI
|
6 |
R. F. Bailey, J. Caceres, D. Garijo, A. Gonzalez, A. Marquezc, K. Meagherd, and M. L. Puertas, Resolving sets for Johnson and Kneser graphs, European J. Combin. 34 (2013), no. 4, 736-751.
DOI
|
7 |
R. F. Bailey and P. J. Cameron, Base size, metric dimension and other invariants of groups and graphs, Bull. Lond. Math. Soc. 43 (2011), no. 2, 209-242.
DOI
|
8 |
R. F. Bailey and K. Meagher, On the metric dimension of Grassmann graphs, Discrete Math. Theor. Comput. Sci. 13 (2011), no. 4, 97-104.
|
9 |
M. Baziar, E. Momtahan, and S. Safaeeyan, A zero-divisor graph for modules with respect to their (first) dual, J. Algebra Appl. 12 (2013), no. 2, 1250151, 11 pp.
DOI
|
10 |
I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208-226.
DOI
|
11 |
F. DeMeyer and K. Schneider, Automorphisms and zero-divisor graphs of commutative rings, Internat. J. Commutative Rings 1 (2002), no. 3, 93-106.
|
12 |
J. Diaz, O. Pottonen, M. Serna, and E. J. van Leeuwen, On the complexity of metric dimension, On the complexity of metric dimension. , 419-430, Lecture Notes in Comput. Sci., 7501, Springer, Heidelberg, 2012.
|
13 |
R. Diestel, Graph Theory, Springer-Verlag, New York, 1997.
|
14 |
P. Erdos and A. Renyi, On two problems of information theory, Magyar Tud. Akad. Mat. Kutato Int. Kozl. 8 (1963), 229-243.
|
15 |
F. Harary and R. A. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976), 191-195.
|
16 |
M. Feng and K. Wang, On the metric dimension of bilinear forms graphs, Discrete Math. 312 (2012), no. 6, 1266-1268.
DOI
|
17 |
Sh. Ghalandarzadeh and P. Malakooti Rad, Torsion graph over multiplication modules, Extracta Math. 24 (2009), no. 3, 281-299.
|
18 |
A. Haghany and M. R. Vedadi, Endoprime modules, Acta Math. Hungar. 106 (2005), no. 1-2, 89-99.
DOI
|
19 |
S. Hoffmann and E Wanke, Metric dimension for Gabriel unit disk graphs is NP-complete, Lecture Notes Comp. Sci. 7718 (2013), 90-92.
|
20 |
S. Khuller, B. Raghavachari, and A. Rosenfeld, Landmarks in graphs. Discrete Appl. Math. 70 (1996), no. 3, 217-229.
DOI
|
21 |
R. Levy and J. Shapiro, The zero-divisor graph of von Neumann regular rings, Comm. Algebra 30 (2002), no. 2, 745-750.
DOI
|
22 |
S. B. Mulay, Cycles and symmetries of zero-divisors, Comm. Algebra 30 (2002), no. 7, 3533-3558.
DOI
|
23 |
S. Pirzada, An Introduction to Graph Theory, Universities Press, OrientBlackSwan, Hyderabad, India, 2012.
|
24 |
S. Pirzada and R. Raja, On the metric dimension of a zero-divisor graph, Comm. Algebra, to appear.
|
25 |
S. Pirzada, R. Raja, and S. P. Redmond, Locating sets and numbers of graphs associated to commutative rings, J. Algebra Appl. 13 (2014), no. 7, 1450047, 18 pages.
|
26 |
R. Raja, S. Pirzada, and S. P. Redmond, On locating numbers and codes of zero-divisor graphs associated with commutative rings, J. Algebra Appl. 15 (2016), no. 1, 1650014, 22 pages.
|
27 |
D. B. West, Introduction to Graph Theory, 2nd ed. USA: Prentice Hall, 2001.
|
28 |
S. P. Redmond, The zero-divisor graph of a noncommutative ring, Internat. J. Commutative Rings 1 (2002), no. 4, 203-211.
|
29 |
S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra 31 (2003), no. 9, 4425-4443.
DOI
|
30 |
S. Safaeeyan, M. Bazair and E. Momtahan, A generalization of the zero-divisor graph for modules, J. Korean Math. Soc. 51 (2014), no. 1, 87-98.
DOI
|
31 |
R. Wisbauer, Foundations of Modules and Ring Theory, Gordon and Breach Reading, 1991.
|