The intersection graph of gamma sets in the total graph of a commutative ring I
نویسندگان
چکیده
Let R be a commutative ring and Z(R) be its set of all zero-divisors. D. F. Anderson and A. Badawi[2] introduced the total graph of R, denoted by TΓ(R), as the undirected graph with vertex set R, and two distinct vertices x and y are adjacent if and only if x+ y ∈ Z(R). For a commutative Artin ring R, T. Tamizh Chelvam and T. Asir[15] obtained the domination number of the total graph and studied certain other domination parameters of TΓ(R). The intersection graph of gamma sets in TΓ(R) is denoted by ITΓ(R). In this paper, we study about ITΓ(R), where R is a commutative Artin ring. At the first instance, we prove that diam(ITΓ(R)) ≤ 2 and gr(ITΓ(R)) ≤ 4. Further, we discuss about the vertex-transitive property of ITΓ(R). Many of the results presented in this paper generalize the results proved for ITΓ(Zn) in [16].
منابع مشابه
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