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首页> 外文期刊>Hormone molecular biology and clinical investigation. >On The Co-Roman Domination in Graphs
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On The Co-Roman Domination in Graphs

机译：Co-Roman统治的图表

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Let G = (V, E) be a graph and let f : V (G) → {0, 1, 2} be a function. A vertex v is said to be protected with respect to f, if f(v) > 0 or f(v) = 0 and v is adjacent to a vertex of positive weight. The function f is a co-Roman dominating function if (i) every vertex in V is protected, and (ii) each v ∈ V with positive weight has a neighbor u ∈ V with f(u) = 0 such that the function fuv : V → {0, 1, 2}, defined by fuv(u) = 1, fuv(v) = f(v) ? 1 and fuv(x) = f(x) for x ∈ V {v, u}, has no unprotected vertex. The weight of f is ω(f) = ∑v∈V f(v). The co-Roman domination number of a graph G, denoted by γcr(G), is the minimum weight of a co-Roman dominating function on G. In this paper, we give a characterization of graphs of order n for which co-Roman domination number is 2n3 ${{2n} over 3}$ or n ? 2, which settles two open problem in [S. Arumugam, K. Ebadi and M. Manrique, Co-Roman domination in graphs, Proc. Indian Acad. Sci. Math. Sci. 125 (2015) 1–10]. Furthermore, we present some sharp bounds on the co-Roman domination number.
机译：让G = (V, E)是一个图形,让f: V (G)→{0,1、2}是一个函数。保护对f,如果f (v) > 0或f (v)= 0和v相邻的顶点是正的重量。函数如果(我)每个顶点在V是保护,和每个v∈(ii)与积极的重量邻居u V f∈(u) = 0的函数fuv: V→{0 1 2},由fuv (u) =1, fuv (v) = f (v) ?{u v,},没有不受保护的顶点。f是ω(f) =∑v∈f (v)。一个图G,用γcr (G),是的最低重量co-Roman主导功能g在这篇文章中,我们给出一个描述图表的co-Roman n控制数量是2 n3 $ {{2 n} / 3} $或n ?2,解决两个开放问题[S。Arumugam, k·伊巴迪和m . Manrique Co-Roman图统治,印度私立高中Sci Proc。。数学。现在一些co-Roman尖锐的界限统治的数字。

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