Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.     

Representation for the Lagrangian numerical differentiation formula involving elementary symmetric functions

By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the error estimate for local approximation. And we also point out that the numerical differentiation formula constructed by Li [J.P. Li, General explicit difference formulas for numerical differentiation, J. Comput. Appl. Math. 183 (2005) 29-52] is actually a special case of the Lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes.     

综合国力的数学建模

本文考虑社会文明与社会导恶现象的制约机制，建立一个综合国力的非线性数学模型，从数学上讨论了相应的二次微分系统的Ｈｏｐｆ分叉，中心与细焦点的判定，极限环的存在唯一性等问题，并对数学结论予以合理解释，把社会相平面划成社发展区域，社会动荡区域和社会崩溃区域，研讨社会走向，确定纳入社会发展区域的途径。     

A bound on the total size of a cut cover

A cycle cover (cut cover) of a graph G is a collection of cycles (cuts) of G that covers every edge of G at least once. The total size of a cycle cover (cut cover) is the sum of the number of edges of the cycles (cuts) in the cover.We discuss several results for cycle covers and the corresponding results for cut covers. Our main result is that every connected graph on n vertices and e edges has a cut cover of total size at most 2e-n+1 with equality precisely when every block of the graph is an odd cycle or a complete graph (other than K₄ or K₈). This corresponds to the result of Fan [J. Combin. Theory Ser. B 74 (1998) 353-367] that every graph without cut-edges has a cycle cover of total size at most e+n-1.     

The number of cycle lengths in graphs of given minimum degree and girth

This paper determines lower bounds on the number of different cycle lengths in a graph of given minimum degree k and girth g. The most general result gives a lower bound of ck^g/8.     

Global secure sets of grid-like graphs

Let G=(V,E) be a graph and S⊆V. The set S is a secure set if ∀X⊆S,|N[X]∩S|≥|N[X]−S|, and S is a global secure set if S is a secure set and a dominating set. The cardinality of a minimum global secure set of G is the global security number of G, denoted γ_s(G). The sets studied in this paper are different from secure dominating sets studied in Cockayne et al. (2003) [3], Grobler and Mynhardt (2009) [8], or Klostermeyer and Mynhardt (2008) [13], which are also denoted by γ_s.In this paper, we provide results on the global security numbers of paths, cycles and their Cartesian products.     

基于实际换热的ORC亚/跨临界综合评价

本文以有机朗肯循环(ORC)跨临界与亚临界工质换热特性最新研究成果为基础,采用热力学指标热源回收(火用)效率,以及经济学中的净现值(NPV)概念,结合换热面积分析,建立了考虑实际换热情况的热力学及经济性模型,更合理、更全面地对亚临界循环与跨临界循环的热力学性能和经济性进行了统一分析,为工程实际中亚临界和跨临界的选择提供...     

图中相互独立的4圈和含4个点的路

设k是一个正整数，G是一个顶点数为|G|=4k的图. 假设σ\-2(G)≥4k-1, 则G有一个支撑子图含k-1个4圈和一条顶点数为4的路，使得所有这些圈和路都是相互独立的. 设G=(V\-1,V \-2;E)是一个二分图使得|V\-1|=|V\-2|=2k. 如果对G中每一对满足x∈V\-1和y∈V\-2的不 相邻的顶点x和y 都有d(x)+d(y)≥2k+1, 则G包含k-1个相互独立的4圈和一条顶点数为4的路，使得所有这些圈和路都是相互独立的，并且此度条件是最好的.