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设m是正整数,证明了:(A)如果b是奇素数,且a=m3-3m,b=3m2-1,c=m2+1, 那么丢番图方程 ax+ by=cz(1)仅有正整数解(x,y,z)=(2,2,3);(B)如果b是奇素数,且 a=m|m4-10m2+5|,b=5m4-10m2+5|,b= 5m4-10m2+1, c=m2+ 1,那么丢番图方程(1)仅有正整数解 (x,y,z)=(2,2,5). 相似文献
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Cayley图的边Hamilton性 总被引:7,自引:0,他引:7
设X是有限群G的一个生成集.Cay(X:G)表示生成集为X的G上的Carley图,其顶点集为G,其边集为所有无序对[a,b]组成的集合,其中a,b∈G,a-1b∈X∪X-1(X-1={x-1|x∈X}).若图的每条边都在的Hamilton圈上,则称图是边-Hamilton图.本文证明了:当G为p-群或Hamilton群时,若X含有G的中心元,则Cay(X:G)是边-Hamilton图. 相似文献
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与任意图(m,r)-正交的(g,f)-因子分解 总被引:4,自引:0,他引:4
原晋江 《数学物理学报(A辑)》2000,20(3):304-308
设g和f是定义在图G的顶点集V(G)上的整值函数.证明了如下结果:设r是一个正整数,G是一个(mg+(m-1)r,mf-(m-1)r)-图,且g(x)≥—1,对x∈V(G).则 G是一个随机(m,r)-正交的(g,f)-可因子化图. 相似文献
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刘春峰 《纯粹数学与应用数学》1998,14(1):42-46
设G是一个简单图,L=u1u2…ut是G中的一个路,定义L的度d(L)=∑ti=1d(ui),其中d(ui)为ui在G中的度数.本文证明了:若G是n≥3阶几乎无桥的简单连通图,GK1,n-1,且对G中任何两个无公共点的二长路L1,L2,有d(L1)+d(L2)≥2n-1,则G有一个D-闭迹,从而G的线图L(G)是Hamilton图. 相似文献
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We define a graph structure associated in a natural way to finite fields that nevertheless distinguishes between different models of isomorphic fields. Certain basic notions in finite field theory have interpretations in terms of standard graph properties. We show that the graphs are connected and provide an estimate of their diameter. An accidental graph isomorphism is uncovered and proved. The smallest non-trivial Laplace eigenvalue is given some attention, in particular for a specific family of 8-regular graphs showing that it is not an expander. We introduce a regular covering graph and show that it is connected if and only if the root is primitive. 相似文献
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Peter Beelen 《Journal of Number Theory》2004,108(2):217-240
In this paper we state and explore a connection between graph theory and the theory of recursively defined towers. This leads, among other things, to a generalization of Lenstra's identity (Finite Fields Appl. 8 (2001) 166) and the solution of an open problem concerning the Deuring polynomial posed in (J. Reine Angew. Math. 557 (2003) 53). Further we investigate the effect extension of the constant field has on the limit of certain towers. 相似文献
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W. R. Pulleyblank 《Mathematical Programming》1979,17(1):91-103
The problem of finding a minimum cardinality set of nodes in a graph which meet every edge is of considerable theoretical as well as practical interest. Because of the difficulty of this problem, a linear relaxation of an integer programming model is sometimes used as a heuristic. In fact Nemhauser and Trotter showed that any variables which receive integer values in an optimal solution to the relaxation can retain the same values in an optimal solution to the integer program. We define 2-bicritical graphs and give several characterizations of them. One characterization is that they are precisely the graphs for which an optimal solution to the linear relaxation will have no integer valued variables. Then we show that almost all graphs are 2-bicritical and hence the linear relaxation almost never helps for large random graphs.This research was supported in part by the National Research Council of Canada. 相似文献
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In this paper, we study the eigenvalue of p-Laplacian on finite graphs. Under generalized curvature dimensional condition, we obtain a lower bound of the first nonzero eigenvalue of p-Laplacian. Moreover, a upper bound of the largest p-Laplacian eigenvalue is derived. 相似文献
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We present a general approach connecting biased Maker‐Breaker games and problems about local resilience in random graphs. We utilize this approach to prove new results and also to derive some known results about biased Maker‐Breaker games. In particular, we show that for , Maker can build a pancyclic graph (that is, a graph that contains cycles of every possible length) while playing a game on . As another application, we show that for , playing a game on , Maker can build a graph which contains copies of all spanning trees having maximum degree with a bare path of linear length (a bare path in a tree T is a path with all interior vertices of degree exactly two in T). © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 47, 615–634, 2015 相似文献
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The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree Δ satisfies some basic expansion properties and contains a family of edge disjoint Hamilton cycles, then there also exists a covering of its edges by Hamilton cycles. This implies that for every α > 0 and every there exists a covering of all edges of G(n,p) by Hamilton cycles asymptotically almost surely, which is nearly optimal.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 183‐200, 2014 相似文献
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Francesco A. Brunacci 《European Journal of Operational Research》1985,19(3):390-396
The archetypal symmetric travelling salesman problem can be seen in a new and interesting way, by using first a standard preparatory phase of input data, and then by applying a transform from the set D of ‘distances’ among ‘cities’ and the set B of ‘loss of optimality’.The specific form of D→B transform is introduced and discussed. In order to show in realistic terms the interest of the approach proposed, a class of ‘diffusive’ heuristic procedures operating from B is defined.An example of solution by an algorithm included in this class is completely worked out; an outline of computational tests done on the same algorithm is also given. 相似文献
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Lucia Gionfriddo 《Discrete Mathematics》2010,310(22):3067-620
A dodecagon quadrangle is the graph consisting of two cycles: a 12-cycle (x1,x2,…,x12) and a 4-cycle (x1,x4,x7,x10). A dodecagon quadrangle system of order n and index ρ [ DQS] is a pair (X,H), where X is a finite set of n vertices and H is a collection of edge disjoint dodecagon quadrangles (called blocks) which partitions the edge set of ρKn, with vertex set X. A dodecagon quadrangle system of order n is said to be perfect [PDQS] if the collection of 4-cycles contained in the dodecagon quadrangles form a 4-cycle system of order n and index μ. In this paper we determine completely the spectrum of DQSs of index one and of PDQSs with the inside 4-cycle system of index one. 相似文献