On generalized gamma near-fields.
On the connectivity of the annihilating-ideal graphs
Let R be a commutative ring with identity and 𝔸*(R) the set of non-zero 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...
Intersection graph of gamma sets in the total graph
In this paper, we consider the intersection graph of gamma sets in the total graph on ℤₙ. We characterize the values of n for which is complete, bipartite, cycle, chordal and planar. Further, we prove that is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivity and some domination parameters of .
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