| Hüseyin Tokat, Alpay Kırlangıç Perfect Roman Domination on Transformation Graphs |
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| Abstract. A dominating set in a graph G is a set of vertices S⊆V(G) such that any vertex of V(G)-S is adjacent to at least one vertex of S. The minimum cardinality of a dominating set is the domination number and denoted by γ(G). The perfect Roman dominating function on a graph G is a function f∶V(G)→{0,1,2} such that for every vertex u with f(u)=0 is adjacent to exactly one vertex v for which f(v)=2. The minimum weight of a perfect Roman dominating function on G is called the perfect Roman domination number of G and denoted by γ_R^P (G). In this paper, we investigate the perfect Roman domination number for the transformation graphs P_n^(---), P_n^(+++) of path graph P_n and C_n^(--+), C_n^(---) of a graph C_n. Moreover we give the perfect Roman domination number of transformation graph G^(--+) of a connected graph G with order n. |
| Keywords: Domination Number, Perfect Roman Domination Number, Transformation Graph |
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| DOI: https://doi.org/10.54381/itta2024.43 |