Abstract. A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial graph. ...

A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, 3, . . .,|V|} such that if an edge uv is assigned the label 1 if f(u) divides f(v) or f(v) divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial graph. ...

In this note we prove that in the case of finitely generated amenable groups the classical zero divisor conjecture implies the analytic zero divisor conjecture of Linnell.

In 1988, Beck [10] introduced the notion of coloring of a commutative ring R. Let G be a simple graph whose vertices are the elements of R and two vertices x and y are adjacent if xy = 0. The graph G is known as the zero divisor graph of R. He conjectured that, the chromatic number χ(G) of G is same as the clique number ω(G) of G. In 1993, Anderson and Naseer [1] gave an example of a commutativ...

The concept of the zero-divisor graph of a commutative ring has been studied by many authors, and the k-zero-divisor hypergraph of a commutative ring is a nice abstraction of this concept. Though some of the proofs in this paper are long and detailed, any reader familiar with zero-divisors will be able to read through the exposition and find many of the results quite interesting. Let R be a com...

A divisor cordial labeling of a graph G with vertex set V vertex G is a bijection f from V to {1, 2, 3, . . . |V|} such that an edge uv is assigned the label 1 if f(u) divides f(v) or f(v)divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial gr...