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Paper IPM / M / 15396  


Abstract:  
Let R be a commutative ring with identity 1 Ì¸= 0. Define the comaximal
graph of R, denoted by CG(R), to be the graph whose vertices are the elements of R,
where two distinct vertices a and b are adjacent if and only if Ra + Rb = R. A vertex a
in a simple graph G is said to be a Smarandache vertex (or Svertex for short) provided
that there exist three distinct vertices x, y, and b (all different from a) in G such that
aâx, aâb, and bây are edges in G but there is no edge between x and y. The main
object of this paper is to study the Svertices of CG(R) and CG2(R) J(R) (or CGJ (R)
for short), where CG2(R) is the subgraph of CG(R) which consists of nonunit elements
of R and J(R) is the Jacobson radical of R. There is also a discussion on a relationship
between the diameter and Svertices of CGJ (R).
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