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On the connectivity of the annihilating-ideal graphs

100%

Chelvam T., Selvakumar K.

Discussiones Mathematicae - General Algebra and Applications

2015

tom 35

nr 2

195-204

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 the vertex connectivity of some annihilating-ideal graphs.

Intersection graph of gamma sets in the total graph

100%

Chelvam T., Asir T.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 2

341-356

In this paper, we consider the intersection graph $I_{Γ}(ℤₙ)$ of gamma sets in the total graph on ℤₙ. We characterize the values of n for which $I_{Γ}(ℤₙ)$ is complete, bipartite, cycle, chordal and planar. Further, we prove that $I_{Γ}(ℤₙ)$ 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 $I_{Γ}(ℤₙ)$.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Discussiones Mathematicae Graph Theory

2 Chelvam T.

1 Asir T.

1 Selvakumar K.

1 2015

1 2012

Wyniki wyszukiwania

On the connectivity of the annihilating-ideal graphs

Intersection graph of gamma sets in the total graph