ON THE CONNECTIVITY OF THE ANNIHILATING-IDEAL GRAPHS
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2015, Vol 35, Issue 2
Abstract
Let R be a commutative ring with identity and A∗(R) the set of nonzero ideals with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) and two distinct vertices I1 and I2 are adjacent if and only if I1I2 = (0). In this paper, we examine the presence of cut vertices and cut sets in the annihilating-ideal graph of a commutative Artinian ring and provide a partial classification of the rings in which they appear. Using this, we obtain the vertex connectivity of some annihilating-ideal graphs.
Authors and Affiliations
T. Tamizh Chelvam, K. Selvakumar
Keywords
Related Articles
- EP ID EP304485
- DOI -
- Views 50
- Downloads 0
BOOLEAN FILTERS IN PSEUDO-COMPLEMENTED ALMOST DISTRIBUTIVE LATTICES
In this paper we have introduced the concept of Boolean filters in a pseudo-complemented Almost Distributive Lattice (pseudo-complemented ADL) and studied their properties. Finally, a Boolean filter is characterized in t...
QUADRATIC APPROXIMATION OF GENERALIZED TRIBONACCI SEQUENCES
In this paper, we give quadratic approximation of generalized Tribonacci sequence {Vn}n≥0 defined by Vn = rVn−1 + sVn−2 + tVn−3 (n ≥ 3) and use this result to give the matrix form of the n-th power of a companion matrix...
TRACE INEQUALITIES FOR POSITIVE SEMIDEFINITE MATRICES
Certain trace inequalities for positive definite matrices are generalized for positive semidefinite matrices using the notion of the group generalized inverse.
HOLOMORPH OF GENERALIZED BOL LOOPS II
The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the...
A NOTE ON IDEAL BASED ZERO-DIVISOR GRAPH OF A COMMUTATIVE RING
In this paper, we consider the ideal based zero divisor graph ΓI (R) of a commutative ring R. We discuss some graph theoretical properties of ΓI (R) in relation with zero divisor graph. We also relate certain parameters...