On friendly index sets of 2-regular graphs

Let G be a graph with vertex set V and edge set E, and let A be an abelian group. A labeling f:V→A induces an edge labeling f^∗:E→A defined by f^∗(xy)=f(x)+f(y). For i∈A, let v_f(i)=card{v∈V:f(v)=i} and e_f(i)=card{e∈E:f^∗(e)=i}. A labeling f is said to be A-friendly if |v_f(i)−v_f(j)|≤1 for all (i,j)∈A×A, and A-cordial if we also have |e_f(i)−e_f(j)|≤1 for all (i,j)∈A×A. When A=Z₂, the friendly index set of the graph G is defined as {|e_f(1)−e_f(0)|:the vertex labelingf is Z₂-friendly}. In this paper we completely determine the friendly index sets of 2-regular graphs. In particular, we show that a 2-regular graph of order n is cordial if and only if n?2 (mod 4).     

Disjoint triangles and quadrilaterals in a graph

Let G be a simple graph of order n and s and k be two positive integers. Brandt et al. obtained the following result: If s?k, n?3s+4(k-s) and σ₂(G)?n+s, then G contains k disjoint cycles C₁,…,C_k satisfying |C_i|=3 for 1?i?s and |C_i|?4 for s<i?k. In the above result, the length of C_i is not specified for s<i?k. We get a result specifying the length of C_i for each s<i?k if n?3s+4(k-s)+3.     

基于三种气化炉的整体煤气化湿化燃气轮机循环热力性能分析

将燃料湿化和空气湿化应用到整体煤气化燃气轮机循环中,以降低NOx排放并有效利用系统低品位热。基于水煤浆、干煤粉及输运床三种气化炉,构建了多种整体煤气化湿化燃气轮机循环,分析了其热力性能并给出了湿化方式建议。研究表明：燃料湿化循环系统效率较高;空气湿化循环燃气轮机比功较大;整体煤气化湿化燃气轮机循环具有利用系统外部中低品...     

A REMARK ON THE ORTHOGONALITY OF A CLASS BIDIMENSIONAL NONSEPARABLE WAVELETS

Let M=(11 1-1).In this paper, a necessary condition and an optimal sufficient condition on the orthogonality of M-wavelets are obtained by the introduction of cycle relat to M.     

Cycle embedding in star graphs with more conditional faulty edges

The star graph is one of the most attractive interconnection networks. The cycle embedding problem is widely discussed in many networks, and edge fault tolerance is an important issue for networks since edge failures may occur when a network is put into use. In this paper, we investigate the cycle embedding problem in star graphs with conditional faulty edges. We show that there exist fault-free cycles of all even lengths from 6 to n! in any n-dimensional star graph S_n (n ? 4) with ?3n − 10 faulty edges in which each node is incident with at least two fault-free edges. Our result not only improves the previously best known result where the number of tolerable faulty edges is up to 2n − 7, but also extends the result that there exists a fault-free Hamiltonian cycle under the same condition.     

Asymptotic behavior of intermediate points in the differential mean value theorem of divided differences with repetitions

By the explicit representation for the divided differences with repetitions involving cycle index of symmetric groups, this paper deals with the asymptotic behavior of the intermediate point of the mean value theorem of divided differences with repetitions. Our results generalize some recent interesting results such as the asymptotic expansions of the immediate points of the Taylor formula and the differential mean value theorem of divided differences with distinct points.     

A note on cycle spectra of line graphs

We show that line graphs G=L(H) with σ₂(G)≥7 contain cycles of all lengths k, 2rad(H)+1≤k≤c(G). This implies that every line graph of such a graph with 2rad(H)≥Δ(H) is subpancyclic, improving a recent result of Xiong and Li. The bound on σ₂(G) is best possible.     

非线性密度制约的Ⅱ类功能反应系统的定性分析

本文对具有非线性密度制约的Ⅱ类功能反应系统进行了定性分析,给出了平衡点全局渐近稳定和存在极限环的充分条件及生态解释,所得结果就其参数空间和相空间而言都是大范围的。     

一类线图的泛圈性

本文的主要结果是:设G是n≥3阶简单图,ε≥2,且不含3度的边,若GC_4,C_5及C_4∪K_1且对任意无公共顶点的两边e_1和e_2,有d(e_1) d(e_2)≥2n-3,则G的线圈L(G)是泛圈图。