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A note on the zero divisor graph of a lattice | ||
| Transactions on Combinatorics | ||
| مقاله 16، دوره 3، شماره 3، آذر 2014، صفحه 51-59 اصل مقاله (163.32 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2014.5626 | ||
| نویسندگان | ||
| T. Tamizh Chelvam* ؛ S. Nithya | ||
| Manonmaniam Sundaranar University | ||
| چکیده | ||
| Let $L$ be a lattice with the least element $0$. An element $x\in L$ is a zero divisor if $x\wedge y=0$ for some $y\in L^*=L\setminus \left\{0\right\}$. The set of all zero divisors is denoted by $Z(L)$. We associate a simple graph $\Gamma(L)$ to $L$ with vertex set $Z(L)^*=Z(L)\setminus \left\{0\right\}$, the set of non-zero zero divisors of $L$ and distinct $x,y\in Z(L)^*$ are adjacent if and only if $x\wedge y=0$. In this paper, we obtain certain properties and diameter and girth of the zero divisor graph $\Gamma(L)$. Also we find a dominating set and the domination number of the zero divisor graph $\Gamma(L)$. | ||
| کلیدواژهها | ||
| zero divisor graph؛ lattice؛ atomic lattice؛ ideal؛ dominating set | ||
| مراجع | ||
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D. D. Anderson and M. Naseer (1993) Beck’s coloring of a commutative ring J. Algebra 150, 500-514
D. F. Anderson and P. Livingston (1999) The zero divisor graph of a commutative ring J. Algebra 217, 434-447
D. F. Anderson, R. Levy and J. Shapiro, (2003) Zero divisor graphs, von Neumann regular rings and Boolean algebras J.
Pure Appl. Algebra 180, 221-241
I. Beck (1988) Coloring of Commutative rings J. Algebra 116, 208-226
B. Bollobos and I. Rival (1979) The maximal size of the covering graph of a lattice Algebra Universalis 9, 371-373
G. Chartrand and P. Zhang (1986) Introduction to Graph theory Wadsworth and Brooks/Cole, Monterey, CA
B. A. Davey and H. A. Priestley (2002) Introduction to Lattices and Order Cambridge University Press, New York
F. R. Demeyer, T. Mckenzie and K. Schneider (2002) The zero divisor graph of a commutative semigroup Semigroup
Forum 65, 206-214
D. Duffus and I. Rival (1977) Path length in the covering graph of a lattice Discrete Math. 19, 139-158
E. Estaji and K. Khashyarmanesh (2012) The zero divisor graph of a lattice, Results Math., DOI
10.1007/s00025-010-0067-8. 61, 1-11
E. Mendelson (2004) Boolean algebra and Switching Circuits Tata McGraw-Hill, New Delhi
N. D. Filipov (1980) Comparability graphs of partially ordered sets of different types Colloq. Math. Soc. J´anos Bolyai 33, 373-380
E. Gedeonov´a (1980) Lattices whose covering graphs are S-graphs Colloq Math. Soc. J´anos Bolyai 33, 407-435
S. K. Nimbhorkar, M. P. Wasadikar and M. M. Pawar (2010) Coloring of lattices Math. Slovaca 60, 419-434
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