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  • 云南民族大學學報(自然科學版)

    2021, v.30;No.127(03) 240-244+250

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    有向圖的Roman k-控制
    Roman k-domination of digraphs

    張曉轉;孟巍;
    ZHANG Xiao-zhuan;MENG Wei;School of Mathematical Sciences, Shanxi University;

    摘要(Abstract):

    設k是一個正整數,稱f:V→{0,1,2}是有向圖D=(V,A)的一個Roman k-控制函數,如果對于每個f(v)=0的頂點v,它至少有k個入鄰點v_1,v_2,…,v_k滿足f(v_1)=f(v_2)=…=f(v_k)=2.Roman k-控制函數f的權值ω(f)是指在f的作用下各個頂點的值的和,即ω(f)=∑_(v∈V)f(v).有向圖D的權值最小的Roman k-控制函數的權值稱作有向圖D的Roman k-控制數,記作γ_({Rk})(D).注意到Roman 1-控制數γ_({R1})(D)就是Roman控制數γ_R(D).首先給出了Roman k-控制數的一些性質,然后給出了一些特殊有向圖的Roman k-控制數的界.
    Let k be a positive integer. For a digraph D=(V,A), a Roman k-dominating function f:V→{0,1,2} has the property that for every vertex v∈V with f(v)=0,v has at least kin-neighbors v_1,v_2,…,v_k with f(v_1)=f(v_2)=…=f(v_k)=2. The weight of a Roman k-dominating function f is the sum of the value of each vertex under function f, that is, ω(f)=∑_(v∈V) f(v). The minimum weight of a Roman k-dominating function is the Roman k-domination number, that is, γ_({Rk})(D). It is crucial that the Roman 1-domination number γ_({R1})(D) is the Roman domination number γ_R(D). First, it gives some properties of the Roman k-domination number. Next, it gives the bounds of the Roman k-domination number for some special digraphs.

    關鍵詞(KeyWords): 有向圖;Roman k-控制函數;Roman k-控制數
    digraphs;Roman k-dominating functions;Roman k-domination number

    Abstract:

    Keywords:

    基金項目(Foundation): 國家自然科學基金(109025901005)

    作者(Author): 張曉轉;孟巍;
    ZHANG Xiao-zhuan;MENG Wei;School of Mathematical Sciences, Shanxi University;

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    DOI:

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