多重跳图的平面性

The infinite sequence {J^k5(G)} where Js(G) denotes the 5-jump graph of G, is planar if, and only if, G=cor(K3). For r-jump graph with r≥6, there does not exist a graph G such that the sequence {J^kr(G)} is planar.     

一类联图的距离谱半径以及盖理论（英文）

令X=(n₁,n₂,…,n_t),Y=(m₁,m₂,…,m_t)是两个t维递减序列.如果对所有的j,1≤j≤t,都有∑_i=1~j、n_i≥∑_i=1~j m_i以及∑_i=1~t n_i=∑_i=1~t m_i,则称X可盖Y,记作X■Y.如果X≠Y,则记作X■Y.本文考虑联图G(n₁,n₂,…,n_t;a)=(K_n1∪_n2∪…∪K_nt)∨K_a的谱半径,这里n₁+n₂+…+n_t+a=n,(n₁,n     

(邻接)树图的同构及平面性

树图是非常有用的一类图.本文刻画了(邻接)树图分别为Pn,Cn,Kn的图类并且讨论了(邻接)树图的平面性.     

3,4跳图的平面性

For a graph G of size ε≥1 and its edge-induced subgraphs H1 and H2 of size r(1≤r≤ε), H1 is said to be obtained from H2 by an edge jump if there exist four distinct vertices u,v,w and x in G such that (u,v)∈E(H2), (w,x)∈ E(G)-E(H2) and H1=H2-(u,v)+(w,x). In this article, the r-jump graphs (r≥3) are discussed. A graph H is said to be an r-jump graph of G if its vertices correspond to the edge induced graph of size r in G and two vertices are adjacent if and only if one of the two corresponding subgraphs can be obtained from the other by an edge jump. For k≥2, the k-th iterated r-jump graph Jrk(G) is defined as Jr(Jrk-1(G)), where Jr1(G)=Jr(G).An infinite sequence{Gi} of graphs is planar if every graph Gi is planar. It is shown that there does not exist a graph G for which the sequence {J3k(G)} is planar, where k is any positive integer. Meanwhile,lim gen(J3k(G))=∞,where gen(G) denotes the genus of a graph G, if the sequencek→∞J3k(G) is defined for every positive integer k. As for the 4-jump gra     

极大外平面图的不可定向强最大亏格

强嵌入猜想称:任意2-连通图都可以强嵌入到某一曲面上．本文通过分析极大外平面图的结构以及强嵌入的特征,讨论了该图类的不可定向强最大亏格,并给出了一个复杂度为O(nlogn)的算法．其中部分图类的强最大亏格嵌入提供该图的一个少双圈覆盖．     

Decycling Number of Some Graphs

1.IntroductionInthispaper,weonlydiscusssimplegraph(withneithermulti-edgenorloop).TheterminologiesnotexplainedcanbeseeninII].Thecyclerankofagraphistheminimumnumberofedgesthatmustberemovedinordertoeliminateallofthecyclesinthegraph.IfGhaspvenices,qedges...     

循环图圈空间的最小基

For most of circular graph the length of the minimum cycle basis is given.For the others a bound of the length of the minimum cycle basis is given and the given bound is reached.     

循环图C(n,m)}的最小亏格

本文给出了所有循环图的可定向与不可定向最小亏格. 同时, 也给出了部分循环图的强最小亏格.     

联图的圈基

MacLane于1937年给出了圈基方面的重要定理: 图G是平面图, 当且仅当图G有2-重基. 连通图G_1和G_2的联图G_1\vee G_2指的是在它们的不交并G_1\bigcup G_2上添加边集(u,v)|u\in V(G_1), v\in V(G_2). 对G_1和G_2的联图G_1\vee G_2的圈基重数进行了研究, 得到了一个上界, 改进了Zare的结果. 并在此基础之上, 进一步得到特殊联图C_m\vee C_n的圈基重数的一个上界.     

G(2m+1,m)的不可定向强最大亏格

图G的最大亏格指图G能嵌入到亏格为k的曲面的最大整数k.对于广义Petersen图G(2m 1,m),当m=1,4(mod 6),给出了最大亏格的表达式,对其余形,给出了不可定向强最大亏格的上界和下界.