共查询到20条相似文献,搜索用时 46 毫秒
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图X称为边正则图,若X的自同构群Aut(X)在X的边集上的作用是正则的.本文考察了三度边正则图与四度Cayley图的关系,给出了一个由四度Cayley图构造三度边正则图的方法,并且构造了边正则图的三个无限族. 相似文献
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大量研究表明,图的主特征值的数量与图的结构有着密切关系.通过恰有两个主特征值的图的特征定义了2-邻域k-剖分图,研究了恰有两个主特征值的图与2-邻域k-剖分图之间的关系;同时给出一个2-邻域k-剖分图在k=2,3时为等部剖分的条件. 相似文献
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设γM(G)是连通图G=(V,E)的最大亏格,记EM^-(G)={e∈E(G)|G\e连通,且γM(G\e)=γM(G)}。若EM^-(G)≠0,则称G是γ(G)-可约的;否则称G是γM(G)-不可约的。本文证明了边的剖分不改变图的最大亏格可约性,点的扩张不改变上可嵌入图的最大亏格可约性;并给出了两类满足EM^-(G)=E(G)的非4-边连通图。 相似文献
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在毁裂度的基础上,研究图的边的毁裂度.通过优化组合、归纳假设的方法界定了图的边毁裂度的值,如笛卡尔积图:Pm×Pn,Pm×Cn,Cm×Cn,Km×Kn,并界定了G=G1×G2的边毁裂度的界.最后给出了一些基本图,如路、圈、星图、完全二部图Km,n的线图边毁裂度. 相似文献
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利用轮子图构造出一类图,证明了这类图都是点传递但边不传递的正则图,并证明了通过覆盖的方法,可以使一类2m2(m>3,m为正整数)阶非边传递图变成对称图,这类对称图实际上是亚循环图. 相似文献
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如果~$k$-\-正则图~$G$~不含~5-\-圈的分支, 则猜测~$\chi''_{\mathrm{as}}(G) = \chi_{\mathrm t}(G)$. 证明这个猜想对很多图类都成立, 例如: 第1类型图、 $2$-\-正则图、$3$-\-正则图、$(|V(G)|-2)$-\-正则图、二部图、完全等多部图、$k$-\-方体以及一些特殊的联图类等. 相似文献
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对简单图G(V,E),f是从V(G)∪E(G)到{1,2,…,k}的映射,k是自然数,若f满足(1)uv,uw∈E(G),u≠w,f(uv)≠f(uw);(2)uv∈E(G),C(u)≠C(v).则称f是G的一个邻强边染色,最小的k称为邻强边色数,其中C(u)={f(uv)|uv∈E(G)}.给出了一类3-正则重圈图的邻强边色数. 相似文献
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Masahiro Ohtani 《代数通讯》2013,41(10):3858-3867
In this article, we prove some results about the binomial edge ideal J G of a complete r-partite graph G = K a 1,…, a r : (1) characterization of unmixedness of J G and Cohen–Macaulayness of the residue ring S/J G , (2) F-purity of S/J G , and (3) the equality of the symbolic and the ordinary powers of J G . 相似文献
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We provide some exact formulas for the projective dimension and regularity of edge ideals associated to some vertex-weighted oriented cyclic graphs with a common vertex or edge.These formulas are functions in the weight of the vertices,and the numbers of edges and cycles.Some examples show that these formulas are related to direction selection and the assumption that w(x)≥2 for any vertex x cannot be dropped. 相似文献
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LI YANG 《数学研究通讯:英文版》2014,(2):183-192
Let G be a complete p-partite graph with 2 edges removed, p ≥ 7, which is intrinsically knotted. Let J represent any graph obtained from G by a finite sequence of △-Y exchanges and/or vertex expansions. In the present paper, we show that the removal of any vertex of J and all edges incident to that vertex produces an intrinsically linked graph. This result offers more intrinsically knotted graphs which hold for the conjecture presented in Adams' book (Adams C. The Knot Book. New York: W. H. Freeman and Company, 1994), that is, the removal of any vertex from an intrinsically knotted graph yields an intrinsically linked graph. 相似文献
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Let G be a complete p-partite graph with 2 edges removed, p ≥ 7, which is intrinsically knotted. Let J represent any graph obtained from G by a finite sequence of ?-Y exchanges and/or vertex expansions. In the present paper, we show that the removal of any vertex of J and all edges incident to that vertex produces an intrinsically linked graph. This result offers more intrinsically knotted graphs which hold for the conjecture presented in Adams' book(Adams C. The Knot Book. New York: W. H. Freeman and Company, 1994), that is, the removal of any vertex from an intrinsically knotted graph yields an intrinsically linked graph. 相似文献
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In this paper, we determine the neighbor connectivity κNB of two kinds of Cayley graphs: alternating group networks AN n and star graphs S n ; and give the exact values of edge neighbor connectivity λNB of ANn and Cayley graphs generated by transposition trees Γ n . Those are κNB(AN n ) = n?1, λNB(AN n ) = n?2 and κNB(S n ) = λNB(Γ n ) = n?1. 相似文献
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Andrew H. Hoefel 《代数通讯》2013,41(4):1222-1233
Let P = 𝕜[x 1,…, x n ] be the polynomial ring in n variables. A homogeneous ideal I ? P generated in degree d is called Gotzmann if it has the smallest possible Hilbert function out of all homogeneous ideals with the same dimension in degree d. The edge ideal of a simple graph G on vertices x 1,…, x n is the quadratic square-free monomial ideal generated by all x i x j where {x i , x j } is an edge of G. The only edge ideals that are Gotzmann are those edge ideals corresponding to star graphs. 相似文献
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