共查询到16条相似文献,搜索用时 375 毫秒
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设图G=G(V,E),令函数f:V→{-1,1},f的权w(f)=∑v∈Vf[v],对v∈V,定义f[v]=∑u∈N[v]f(u),这里N[v]表示V中顶点v及其邻点的集合。图G的符号控制函数为f:V→{-1,1}满足对所有的v∈V有f[v]≥1,图G的符号控制数γs(G)就是图G上符号控制数的最小权,称其f为图G的γs-函数。研究了C2n图,通过给出它的一个γs-函数得到了其符号控制数。 相似文献
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设G=(V,E)是一个图,一个函数f:V∪E→{-1,+}1,如果对每一个x∈E∪V,都有∑y∈Nt[x]f(y)≤0成立,则称f为图G的一个反符号全控制函数,其中Nt(x)表示G中与元素x相邻或相关联的元素之集,称为元素x的全邻域,Nt[x]=N(x)∪{x}为x的闭全邻域。规定图G的反符号全控制数定义为γrst(G)=max{∑x∈V∪Ef(x)f为图的反符号全控制函数}。得到了一般图的反符号全控制数的若干上界,并确定了圈Cn的反符号全控制数。 相似文献
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设图G=G(V,E),令函数f:E→{-1,1},f的权w(f)=∑x∈Ef[x],对x∈E中任一元素,定义f[x]=∑y∈N[x]f(y),这里N[x]表示E中x及其关联边的集合.图G的边符号控制函数为f:E→{-1,1},满足对所有的x∈E有f[x]≥1,图G的边符号控制数γS(G)就是图G上边符号控制数的最小权,称其f为图G的γS-函数.本文得到了Petersen图类的边符号控制数. 相似文献
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设G=(V,E)是一个非空图,一个函数f:E→{-1,1},如果满足∑e’∈N[e]f(e’)≥1对于每一条边e∈E(G)均成立,则称f为图G的一个符号边控制函数。图G的符号边控制数记为r’s(G),定义为r’s(G)=min{∑e∈E(G)f(e)︱f}为G的一个符号边控制函数。全文对图的符号边控制函数进行了研究,得到了图的符号边控制数的若干新的下界。 相似文献
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几乎正则图的全符号控制 总被引:1,自引:2,他引:1
1IntroductionFor notation and graph theory terminology we ingeneral follow[1].LetG=(V,E)be a graph with thevertex setVand the edge setE,andletvbe a vertexinV.The open neighborhood ofvisN(v)={u∈V|uv∈E}and the closed neighborhood ofvisN[v]={v}∪N(v).The d… 相似文献
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图的符号全划分数 总被引:1,自引:0,他引:1
Let G = (V, E) be a graph, and let f : V →{-1, 1} be a two-valued function. If ∑x∈N(v) f(x) ≥ 1 for each v ∈ V, where N(v) is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi(x) ≤ 1 for each x ∈ V, is called a signed total dominating family (of functions) on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s(G). The properties of the signed total domatic number dt^s(G) are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs. 相似文献
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令γ(G)表示一个图G的控制数,G×H表示图G和图H的笛卡尔乘积.现已有很多控制数的研究文章,参考已有控制数知识及笛卡尔乘积图Cm×Cn,Pm×Pn的控制数的相关结论,利用γ(Cm×Cn)≤γ(Pm×Cn)≤γ(Pm×Pn)这一不等式给出路与圈的笛卡尔乘积图Cm×Pn(m=2,3,4),Pm×Cn(m=2,3,4)的控制数. 相似文献
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The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graph theory. In this paper, it was shown that the power domination number of an outerplanar graph with the diameter two or a 2-connected outerplanar graph with the diameter three is precisely one. Upper bounds on the power domination number for a general planar graph with the diameter two or three were determined as an immediate consequences of results proven by Dorfling, et al. Also, an infinite family of outerplanar graphs with the diameter four having arbitrarily large power domination numbers were given. 相似文献
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令图G是无孤立点的无向图。 V(G)是图G的顶点集,D是V(G)的真子集。如果图G的每一个顶点至少与集合D中一点相邻,则集合D是图G的全控制集。 G中最小全控制集的顶点数称为G的全控制数,记为γt(G)。参考已有全控制数的知识及笛卡尔乘积 Cm□Cn、Pm□Pn 的全控制数的相关结论,利用γt(Cm□Cn )≤γt(Pm□Cn )≤γt(Pm□Pn )这一不等式给出了Cm□Pn(m =3,4)、Pm□Cn(n =2,4)的全控制数。 相似文献