1 research outputs found
Independent sets of some graphs associated to commutative rings
Let be a simple graph. A set is independent set of
, if no two vertices of are adjacent. The independence number
is the size of a maximum independent set in the graph. %An
independent set with cardinality Let be a commutative ring with nonzero
identity and an ideal of . The zero-divisor graph of , denoted by
, is an undirected graph whose vertices are the nonzero
zero-divisors of and two distinct vertices and are adjacent if and
only if . Also the ideal-based zero-divisor graph of , denoted by
, is the graph which vertices are the set {x\in R\backslash I |
xy\in I \quad for some \quad y\in R\backslash I\} and two distinct vertices
and are adjacent if and only if . In this paper we study the
independent sets and the independence number of and .Comment: 27 pages. 22 figure