On total directed graphs of non-commutative rings

For a non-commutative ring , the left total directed graph of is a directed graph with vertex set as and for the vertices and , is adjacent to if and only if there is a non-zero which is different from and , such that is a left zero-divisor of . In this paper, we discuss some very basic results of left (as well as right) total directed graph of . We also study the coloring of left total directed graph of directed graph

Center of Intersection Graph of Fuzzy Submodules of Modules

In this paper, we discuss the graphical aspects of fuzzy algebra. Let M be an R−module with zero element θ and F(M) be collection of all fuzzy submodules of M. The intersection graph of F(M) is an undirected graph G with vertex set as F(M) and two vertices α and β are adjacent if and only if α∩β≠χθ, where χθ is the characteristic function on θ. We find the girth of G and also study some properties of center of G−χθ