Paper Information

Journal:   TRANSACTIONS ON COMBINATORICS   2014 , Volume 3 , Number 3; Page(s) 51 To 59.
 
Paper: 

A NOTE ON THE ZERO DIVISOR GRAPH OF A LATTICE

 
 
Author(s):  TAMIZH CHELVAM T.*, NITHYA S.
 
* DEPARTMENT OF MATHEMATICS, MANONMANIAM SUNDARANAR UNIVERSITY, TIRUNELVELI 627012, TAMIL NADU, INDIA
 
Abstract: 

Let L be a lattice with the least element 0. An element x ? L is a zero divisor if x ^ y= 0 for some y ?I L*= L\ {0}. The set of all zero divisors is denoted by Z (L). We associate a simple graph G(L) to L with vertex set Z (L)*= Z (L)\ {0}, the set of non-zero zero divisors of L and distinct x, y ? Z (L)* are adjacent if and only if x ^ y= 0. In this paper, we obtain certain properties and diameter and girth of the zero divisor graph G(L). Also we find a dominating set and the domination number of the zero divisor graph G(L).

 
Keyword(s): ZERO DIVISOR GRAPH, LATTICE, ATOMIC LATTICE, IDEAL, DOMINATING SET
 
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