### On generalized gamma near-fields.

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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...

In this paper, we consider the intersection graph ${I}_{\Gamma}\left(\mathbb{Z}\u2099\right)$ of gamma sets in the total graph on ℤₙ. We characterize the values of n for which ${I}_{\Gamma}\left(\mathbb{Z}\u2099\right)$ is complete, bipartite, cycle, chordal and planar. Further, we prove that ${I}_{\Gamma}\left(\mathbb{Z}\u2099\right)$ 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 ${I}_{\Gamma}\left(\mathbb{Z}\u2099\right)$.

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