A Note on the Double Total Graph Tu(Γ(R)) and Tu(Γ(Zn×Zm))

Authors

  • Ngangom Rojitkumar Singh Department of Mathematics, North-Eastern Hill University, Shillong
  • Sanghita Dutta Department of Mathematics, North-Eastern Hill University, Shillong

DOI:

https://doi.org/10.26713/cma.v12i1.1466

Keywords:

Fusible ring, Weakly unit fusible ring, Unit graph, Total graph, Double total graph

Abstract

Considering a commutative ring R with unity as the set of vertices and two vertices x and y are adjacent if and only if u+(x+y)Z(R) for some uU(R), the resulting graph Tu(Γ(R)) is known as the double total graph. In this paper we find the degree of any vertex in Tu(Γ(R)) for a weakly unit fusible ring R and domination number of Tu(Γ(R)) for any ring R. Also, we investigate the properties of Tu(Γ(Zn×Zm)) and characterize $R$ in terms of toroidal Tu(Γ(R)).

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References

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N. R. Singh and S. Dutta, The double total graph of a commutative ring, Advances and Applications in Discrete Mathematics 24(2) (2020), 99 – 115, DOI: 10.17654/DM024020099.

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Published

31-03-2021
CITATION

How to Cite

Singh, N. R., & Dutta, S. (2021). A Note on the Double Total Graph Tu(Γ(R)) and Tu(Γ(Zn×Zm)). Communications in Mathematics and Applications, 12(1), 203–211. https://doi.org/10.26713/cma.v12i1.1466

Issue

Section

Research Article