Geodesic
Complement of the generalized total graph of Z n
Filomat, Tome 33 (2019) no. 18, p. 6103

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DOI

Let R be a commutative ring with identity and H be a nonempty proper multiplicative prime subset of R. The generalized total graph of R is the (undirected) simple graph GT H (R) with all elements of R as the vertex set and two distinct vertices x and y are adjacent if and only if x + y ∈ H. The complement of the generalized total graph GT H (R) of R is the (undirected) simple graph with vertex set R and two distinct vertices x and y are adjacent if and only if x + y H. In this paper, we investigate certain domination properties of GT H (R). In particular, we obtain the domination number, independence number and a characterization for γ-sets in GT P (Z n) where P is a prime ideal of Z n. Further, we discuss properties like Eulerian, Hamiltonian, planarity, and toroidality of GT P (Z n)
DOI : 10.2298/FIL1918103T
Classification : 05C75, 05C25, 13A15, 13M05
Keywords: commutative rings, total graph, complement, domination, gamma sets, planar, toroidal 
T Tamizh Chelvam; M Balamurugan. Complement of the generalized total graph of Z n. Filomat, Tome 33 (2019) no. 18, p. 6103 . doi: 10.2298/FIL1918103T
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     title = {Complement of the generalized total graph of {Z} n},
     journal = {Filomat},
     pages = {6103 },
     year = {2019},
     volume = {33},
     number = {18},
     doi = {10.2298/FIL1918103T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL1918103T/}
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