共查询到20条相似文献,搜索用时 546 毫秒
1.
A total [k]-coloring of a graph G is a mapping φ: V(G) U E(G) →{1, 2, ..., k} such that any two adjacent elements in V(G)UE(G) receive different colors. Let f(v) denote the sum of the colors of a vertex v and the colors of all incident edges of v. A total [k]-neighbor sum distinguishing-coloring of G is a total [k]-coloring of G such that for each edge uv E E(G), f(u) ≠ f(v). By tt [G, Xsd( J, we denote the smallest value k in such a coloring of G. Pilniak and Woniak conjectured X'sd(G) 〈 A(G) + 3 for any simple graph with maximum degree A(G). This conjecture has been proved for complete graphs, cycles, bipartite graphs, and subcubic graphs. In this paper, we prove that it also holds for Ka-minor free graphs. Furthermore, we show that if G is a Ka-minor flee graph with A(G) 〉 4, then " Xnsd(G) 〈 A(G) + 2. The bound A(G) + 2 is sharp. 相似文献
2.
Czechoslovak Mathematical Journal - Let G = (V(G), E(G)) be a simple graph and EG(υ) denote the set of edges incident with a vertex υ. A neighbor sum distinguishing (NSD) total coloring... 相似文献
3.
设f:V(G)∪E(G)→{1,2,…,k}是图G的一个正常k-全染色。令■其中N(x)={y∈V(G)|xy∈E(G)}。对任意的边uv∈E(C),若有Φ(u)≠Φ(v)成立,则称f是图G的一个邻点全和可区别k-全染色。图G的邻点全和可区别全染色中最小的颜色数k叫做G的邻点全和可区别全色数,记为f tndi∑(G)。本文确定了路、圈、星、轮、完全二部图、完全图以及树的邻点全和可区别全色数,同时猜想:简单图G(≠K2)的邻点全和可区别全色数不超过△(G)+2。 相似文献
4.
Josef Bukac 《逼近论及其应用》2008,(4):330-335
Minimization of the weighted nonlinear sum of squares of differences may be converted to the minimization of sum of squares. The Gauss-Newton method is recalled and the length of the step of the steepest descent method is determined by substituting the steepest descent direction in the Gauss-Newton formula. The existence of minimum is shown. 相似文献
5.
Yanjun YAO 《Frontiers of Mathematics in China》2014,9(5):1131-1140
We prove that each sufficiently large odd integer N can be written as sum of the form N = p1^3 +p2^3 +... +p9^3 with [pj - (N/9)^1/31 ≤ N^(1/3)-θ, where pj, j = 1,2,...,9, are primes and θ = (1/51) -ε. 相似文献
6.
Bojan BAI 《数学学报(英文版)》2014,30(4):689-695
We characterize all functions f :N → C such thatf(m2+n2)=f(m)2+f(n)2for all m,n∈ N.It turns out that all such functions can be grouped into three families,namelyf≡0,f(n)=±n(subject to some restrictions on when the choice of the sign is possible) and f(n)=±1/2(again subject to some restrictions on when the choice of the sign is possible). 相似文献
7.
ZHANG TIAN-PING 《东北数学》2009,25(4):329-339
The main purpose of this paper is to use the analytic methods to study the hybrid mean value involving the hyper Cochrane sums, and give several sharp asymptotic formulae. 相似文献
8.
Letk be a positive integer and n a nonnegative integer,0 λ1,...,λk+1 ≤ 1 be real numbers and w =(λ1,λ2,...,λk+1).Let q ≥ max{[1/λi ]:1 ≤ i ≤ k + 1} be a positive integer,and a an integer coprime to q.Denote by N(a,k,w,q,n) the 2n-th moment of(b1··· bk c) with b1··· bk c ≡ a(mod q),1 ≤ bi≤λiq(i = 1,...,k),1 ≤ c ≤λk+1 q and 2(b1+ ··· + bk + c).We first use the properties of trigonometric sum and the estimates of n-dimensional Kloosterman sum to give an interesting asymptotic formula for N(a,k,w,q,n),which generalized the result of Zhang.Then we use the properties of character sum and the estimates of Dirichlet L-function to sharpen the result of N(a,k,w,q,n) in the case ofw =(1/2,1/2,...,1/2) and n = 0.In order to show our result is close to the best possible,the mean-square value of N(a,k,q) φk(q)/2k+2and the mean value weighted by the high-dimensional Cochrane sum are studied too. 相似文献
9.
林群 《数学的实践与认识》2008,38(12):202-204
复杂事物常表现为整体和部分之间的关系,简单说,整体比=部分比的平均,精确说,a1+a2+…/b1+b2…=(a1/b1,a2/b2…)的平均(这里b>0).微积分的基本定理就是一例:曲线小段求高造成了小误差;曲线全段(小段的和)求高造成了全误差(小误差的和);取部分比=小误差/小段,则整体比=小误差的和/小段的和=小误差/小段的平均 相似文献
10.
Neighbor sum distinguishing total colorings of triangle free planar graphs 总被引:1,自引:0,他引:1 下载免费PDF全文
A total k-coloring c of a graph G is a proper total coloring c of G using colors of the set[k] = {1, 2,..., k}. Let f(u) denote the sum of the color on a vertex u and colors on all the edges incident to u. A k-neighbor sum distinguishing total coloring of G is a total k-coloring of G such that for each edge uv ∈ E(G), f(u) = f(v). By χ nsd(G), we denote the smallest value k in such a coloring of G. Pil′sniak and Wo′zniak conjectured that χ nsd(G) ≤Δ(G) + 3 for any simple graph with maximum degree Δ(G). In this paper, by using the famous Combinatorial Nullstellensatz, we prove that the conjecture holds for any triangle free planar graph with maximum degree at least 7. 相似文献
11.
Let Mi be a compact orientable 3-manifold, and Ai a non-separating incompressible annulus on a component of δMi, say Fi, i = 1, 2. Let h : A1 → A2 be a homeomorphism, and M→M1 ∪h M2, the annulus sum of Mi and M2 along A1 and A2. Suppose that Mi has a Heegaard splitting Vi ∪Si Wi with distance d(Si) ≥ 2g(Mi) + 2g(F3-i) + 1, i = 1, 2. Then g(M) = g(M1) + g(M2), and the minimal Heegaard splitting of M is unique, which is the natural Heegaard splitting of M induced from Vi∪S1 Wi and V2 ∪S2 W2. 相似文献
12.
Wen Sheng Wang 《数学学报(英文版)》2014,30(9):1555-1565
Let θ∈ Rdbe a unit vector and let X,X1,X2,...be a sequence of i.i.d.Rd-valued random vectors attracted to operator semi-stable laws.For each integer n ≥ 1,let X1,n ≤···≤ Xn,n denote the order statistics of X1,X2,...,Xn according to priority of index,namely | X1,n,θ | ≥···≥ | Xn,n,θ |,where ·,· is an inner product on Rd.For all integers r ≥ 0,define by(r)Sn = n-ri=1Xi,n the trimmed sum.In this paper we investigate a law of the iterated logarithm and limit distributions for trimmed sums(r)Sn.Our results give information about the maximal growth rate of sample paths for partial sums of X when r extreme terms are excluded.A stochastically compactness of(r)Sn is obtained. 相似文献
13.
Let G=(V,E)be a graph andφbe a total coloring of G by using the color set{1,2,...,k}.Let f(v)denote the sum of the color of the vertex v and the colors of all incident edges of v.We say thatφis neighbor sum distinguishing if for each edge uv∈E(G),f(u)=f(v).The smallest number k is called the neighbor sum distinguishing total chromatic number,denoted byχ′′nsd(G).Pil′sniak and Wo′zniak conjectured that for any graph G with at least two vertices,χ′′nsd(G)(G)+3.In this paper,by using the famous Combinatorial Nullstellensatz,we show thatχ′′nsd(G)2(G)+col(G)-1,where col(G)is the coloring number of G.Moreover,we prove this assertion in its list version. 相似文献
14.
设f是图G的一个正常全染色.对任意x∈V(G),令C(x)表示与点x相关联或相邻的元素的颜色以及点x的颜色所构成的集合.若对任意u,v∈V(G),u≠v,有C(u)≠C(v),则称.f是图G的一个点强可区别全染色,对一个图G进行点强可区别全染色所需的最少的颜色的数目称为G的点强可区别全色数,记为X_(vst)(G).讨论了完全二部图K_(1,n),K_(2,n)和L_(3,n)的点强可区别全色数,利用组合分析法,得到了当n≥3时,X_(vst)(K_(1,n)=n+1,当n≥4时,X_(vst)(K_(2,n)=n+2,当n≥5时,X_(vst)(K_(3,n))=n+2. 相似文献
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16.
Pil?niak and Wo?niak put forward the concept of neighbor sum distinguishing (NSD) total coloring and conjectured that any graph with maximum degree Δ admits an NSD total (Δ+3)-coloring in 2015. In 2016, Qu et al. showed that the list version of the conjecture holds for any planar graph with Δ ≥ 13. In this paper, we prove that any planar graph with Δ ≥ 7 but without 6-cycles satisfies the list version of the conjecture. 相似文献
17.
A proper edge coloring of a graph G without isolated edges is neighbor‐distinguishing if any two adjacent vertices have distinct sets consisting of colors of their incident edges. The neighbor‐distinguishing index of G is the minimum number ndi(G) of colors in a neighbor‐distinguishing edge coloring of G. Zhang, Liu, and Wang in 2002 conjectured that if G is a connected graph of order at least 6. In this article, the conjecture is verified for planar graphs with maximum degree at least 12. 相似文献
18.
Igor Bogluev 《计算数学(英文版)》2013,(6):620-637
This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the ac- celerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform convergence of the monotone weighted average iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented. 相似文献
19.
A proper k-edge coloring of a graph G is an assignment of one of k colors to each edge of G such that there are no two edges with the same color incident to a common vertex. Let f(v) denote the sum of colors of the edges incident to v. A k-neighbor sum distinguishing edge coloring of G is a proper k-edge coloring of G such that for each edge uv∈E(G), f(u)≠f(v). By χ'_∑(G), we denote the smallest value k in such a coloring of G. Let mad(G) denote the maximum average degree of a graph G. In this paper, we prove that every normal graph with mad(G) ■ and Δ(G) ≥ 8 admits a(Δ(G) + 2)-neighbor sum distinguishing edge coloring. Our approach is based on the Combinatorial Nullstellensatz and discharging method. 相似文献
20.
A sequential effect algebra (E, 0, 1, ,o) is an effect algebra on which a sequential product o with certain physics properties is defined; in particular, sequential effect algebra is an important model for studying quantum measurement theory. In 2005, Gudder asked the following problem: If a, b E (E, 0, 1, , o) and a⊥b and a o b⊥a o b, is it the case that 2(a o b) ≤ a2 b2 ? In this paper, we construct an example to answer the problem negatively. 相似文献