Nonseparating Independent Sets and Maximum Genus of Graphs

Acta Mathematicae Applicatae Sinica, English Series - A subset I of vertices of an undirected connected graph G is a nonseparating independent set (NSIS) if no two vertices of I are adjacent and G...     

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.     

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     

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.     

The genus distributions for a certain type of permutation graphs in orientable surfaces

A circuit is a connected nontrivial 2-regular graph.A graph G is a permutation graph over a circuit C,if G can be obtained from two copies of C by joining these two copies with a perfect matching.In this paper,based on the joint tree method introduced by Liu,the genus polynomials for a certain type of permutation graphs in orientable surfaces are given.     

基于酸性离子液体的原位泡腾辅助微萃取法测定饮料与糖果中的亮蓝和赤藓红

利用酸性离子液体1-丁基-3-甲基咪唑硫酸氢盐（［C4MIM］［HSO4］）的阴离子与碳酸盐反应产生二氧化碳,通过气泡促进萃取过程。在萃取的同时,［C4MIM］［HSO4］的阳离子和六氟磷酸铵（NH4PF6）原位反应形成疏水性的离子液体1-丁基-3-甲基咪唑六氟磷酸盐（［C4MIM］［PF6］）,从而与水相分离,通过离心收集萃取相,建立了一种基于酸性离子液体的原位泡腾辅助微萃取饮料与糖果样品中亮蓝和赤藓红的方法。考察了酸性离子液体、碳酸氢钠和盐用量对2种色素萃取效率的影响,得到最佳条件为酸性离子液体用量400 mg,碳酸氢钠用量0.4 g,盐用量1.5 g。采用最优条件,目标物亮蓝与赤藓红的质量浓度在0.005 ~ 5 μg/mL范围内呈良好的线性关系,相关系数不小于0.993 3,检出限（LOD）和定量下限（LOQ）分别为0.002 ~ 0.005 μg/mL和0.007 ~ 0.017 μg/mL,日内和日间相对标准偏差（RSD）为2.2% ~ 8.7%。在0.05、0.5 μg/mL 2个加标水平下,回收率为92.2% ~ 107%。所建方法成功用于饮料和糖果样品中2种目标色素的检测。该方法环保、简单且准确,可用于饮料和糖果样品中亮蓝与赤藓红的测定。     

Maximum Genus of Strong Embeddings

The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover.Conversely, it is not true. But for a 3-regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph.     

The Characterization of p-factor-critical Graphs

A graph G is said to be p-factor-critical if G-u₁-u₂-···-up has a perfect matching for any u₁, u₂, ···, u_p ∈ V(G). The concept of p-factor-critical is a generalization of the concepts of factor-critical and bicritical for p = 1 and p = 2, respectively. Heping Zhang and Fuji Zhang[Construction for bicritical graphs and k-extendable bipartite graphs, Discrete Math., 306(2006) 1415–1423] gave a concise structure characterization of bicritical g...