Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE INDEPENDENCE AND INDEPENDENT DOMINATING NUMBERS OF THE TOTAL GRAPH OF A FINITE COMMUTATIVE RING

  • Abughazaleh, Baha' (Department of Mathematics Isra University) ;
  • Abughneim, Omar AbedRabbu (Department of Mathematics The University of Jordan)
  • Received : 2021.10.19
  • Accepted : 2022.01.14
  • Published : 2022.10.01
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Abstract

Let R be a finite commutative ring with nonzero unity and let Z(R) be the zero divisors of R. The total graph of R is the graph whose vertices are the elements of R and two distinct vertices x, y ∈ R are adjacent if x + y ∈ Z(R). The total graph of a ring R is denoted by 𝜏(R). The independence number of the graph 𝜏(R) was found in [11]. In this paper, we again find the independence number of 𝜏(R) but in a different way. Also, we find the independent dominating number of 𝜏(R). Finally, we examine when the graph 𝜏(R) is well-covered.

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References

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