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- Title
Domination and Independence Parameters in the Total Graph of Zn with respect to Nil Ideal.
- Authors
Mishra, Arijit; Patra, Kuntala
- Abstract
For any non-reduced ring Zn, the total graph of Zn with respect to nil ideal, denoted by T(ΓN(Zn)), is a simple, undirected graph having vertex set Zn and any two distinct vertices x and y of T(ΓN(Zn)) are adjacent if and only if x + y ε N(Zn), where N(Zn) = fx ε Zn : x² = 0g denotes the nil ideal of Zn. In this paper, we attempt to find the domination and independence numbers, domatic number and independence domination numbers of T(ΓN(Zn)) and T(ΓN(Zn)), the complement of the total graph of Zn. We also obtain the number of γ-sets and independent sets of these graphs.
- Subjects
INDEPENDENT sets; UNDIRECTED graphs; INDEPENDENCE (Mathematics); DOMINATING set
- Publication
IAENG International Journal of Applied Mathematics, 2020, Vol 50, Issue 3, p203
- ISSN
1992-9978
- Publication type
Article