High dose palliative radiotherapy in NSCLC; 27Gy/6# and 39Gy/13# – is there equivalence?

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• 作者：S. Jain ; G. Hanna ; J. McAleese
• 关键词：Homogeneous factorisations ; Lexicographic products ; Cartesian products ; Direct products
• 刊名：Lung Cancer
• 出版年：2008
• 出版时间：April 2008
• 年：2008
• 卷：60
• 期：Supplement 1
• 页码：S26-S27
• 全文大小：49 K

文摘

A homogeneous factorisation of a digraph Γ consists of a partition of the arc set a1a08c"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">AΓ and two vertex-transitive subgroups MGAut(Γ) such that M fixes each a1a19"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">P_i setwise while G leaves invariant and permutes its parts transitively. Given two graphs Γ₁ and Γ₂ we consider several ways of taking a product of Γ₁ and Γ₂ to form a larger graph, namely the direct product, cartesian product and lexicographic product. We provide many constructions which enable us to lift homogeneous factorisations or certain arc partitions of Γ₁ and Γ₂, to homogeneous factorisations of the various products.