共查询到19条相似文献,搜索用时 828 毫秒
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《数学的实践与认识》2015,(13)
设k是一个非负整数,G是一个p点q边图.如果将G的边用k,k+1,k+2,…,k+q-1进行标号,而顶点标号模p运算后各不相同,那么称图G是后一边优美的.记EGI(G)是所有满足G是k-边优美的k的集合,称EGI(G)是G的边优美指标集.主要是研究n为偶数时W(4,n)的边优美指标集. 相似文献
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令简单图G=(V,E)是有p个顶点q条边的图.假设G的顶点和边由1,2,…,p+q所标号,且f:V ∪E→{1,2,…,p+q}是一个双射,如果对所有的边xy,f(x)+f(y)+f(xy)是常量,则称图G是边幻图(edge-magic).本文证明了三路树P(m,n,t)当n为偶数,t=n+2时也是边幻图. 相似文献
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令简单图G=(V,E)是有p个顶点q条边的图.假设G的顶点和边由1,2,…,p+q所标号,且f:V∪E→{1,2,…,p+q}是一个双射,如果对所有的边xy,f(x)+f(y)+f(xy)是常量,则称图G是边幻图(edge-magic).本文证明了三路树P(m,n,t)当n为偶数,t=n+2时也是边幻图. 相似文献
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设G是m阶连通图,Pm是m个顶点的路.令Skm+1G(i)表示把kG的每一个分支的第i(1≤i≤m)个顶点依次与星图Sk+1的k个1度顶点重迭后得到的图;令Gi1S*(q,km)表示q阶图G的顶点Vi1与Skm+1p(1)的k度顶点重迭后得到的图 相似文献
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<正>大家都知道一个定理:"等高三角形的面积之比等于底边之比".本文目的是充分利用这一性质,探求等积四边形的个数.例1如图1的四边形ABCD,它的面积为S,且AE∶EB=CF∶FD=p∶q,则S四边形AECF=p p+qS 1S四边形EBFD=q p+q2图1图2分析与解在图1中,连结AF、AC及EC,得图2,据题设可知:因AB=AE+EB,CD=CF+FD,故AE∶AB=p∶(p+q),且CF∶CD=p∶(p+q),于是由定理得S△AEC∶S△ABC=p∶(p+q).故S△AEC=p p+qS△ABC, 相似文献
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在数列教学中引入等差数列和等比数列的线性递推式 ,可以为求数列的通项公式提供一些灵活多变的方法 .由递推法求数列的通项有一定的技巧 ,本文介绍通过递推式的变换转化成等差、等比数列求解的几种简单递推数列通项的求法 .1 an+ 1=pan+q型 (其中 p,q为常数 )在此类型中 1当 p =1时是等差数列 ;2当 p≠ 0且 q =0时是等比数列 .在一般情况下 ( p≠ 1 ,q≠ 0 )可向这两种特殊情况转化 .注意到递推式是关于 an+ 1,an 的一次式 ,要想消去 q,可类似解析几何中的坐标平移变换 ,只须令 bn =an + k( k为任意常数 )代入递推式 ,给 k一个适当值即可… 相似文献
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韩广国 《高校应用数学学报(A辑)》2007,22(4):483-490
分类自同构群的基柱为李型单群E8(q)的区传递2-(v,k,1)设计,得到如下定理:设D为一个2-(v,k,1)设计,G≤Aut(D)是区传递、点本原但非旗传递的.若q〉24√(krk-kr+1)f(这里kr=(k,v-1),q=p^f,p是素数,f是正整数),则Soc(G)≌/E8(q). 相似文献
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OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U6(2) 总被引:1,自引:0,他引:1
Let G be a finite group and π(G) = { p 1 , p 2 , ··· , p k } be the set of the primes dividing the order of G. We define its prime graph Γ(G) as follows. The vertex set of this graph is π(G), and two distinct vertices p, q are joined by an edge if and only if pq ∈π e (G). In this case, we write p ~ q. For p ∈π(G), put deg(p) := |{ q ∈π(G) | p ~ q }| , which is called the degree of p. We also define D(G) := (deg(p 1 ), deg(p 2 ), ··· , deg(p k )), where p 1 < p 2 < ··· < p k , which is called the degree pattern of G. We say a group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and degree pattern as G. Specially, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Let L := U 6 (2). In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S 3 is 5-fold OD-characterizable. 相似文献
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Peter J. Slater 《Discrete Mathematics》1981,34(2):185-193
The concept of a k-sequential graph is presented as follows. A graph G with ∣V(G)∪ E(G)∣=t is called k-sequential if there is a bijection such that for each edgein E(G) one has. A graph that is 1-sequential is called simply sequential, and, in particular the author has conjectured that all trees are simply sequential. In this paper an introductory study of k-sequential graphs is made. Further, several variations on the problems of gracefully or sequentially numbering the elements of a graph are discussed. 相似文献
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关于奇强协调图的一些结果 总被引:1,自引:1,他引:0
刘广军 《数学的实践与认识》2013,43(11)
对于一个(p,q)-图G,如果存在一个单射f:V(G)→{0,1,…,2q-1},使得边标号集合{f(uv)|uv∈E(G)}={1,3,5,…,2q-1},其中边标号为f(uv)=f(u)+f(v),那么称G是奇强协调图,并称f是G的一个奇强协调标号.通过研究若干奇强协调图,得出一些奇强协调图的性质. 相似文献
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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
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DU Beiliang WANG Jian Department of Mathematics Suzhou University Suzhou China Nantong Vocational College Nantong China 《中国科学A辑(英文版)》2004,47(3)
Let K_(m,n) be a complete bipartite graph with two partite sets having m and nvertices, respectively. A K_(p,q)-factorization of K_(m,n) is a set of edge-disjoint K_(p,q)-factorsof K_(m,n) which partition the set of edges of K_(m,n). When p=i and q is a prime number,Wang, in his paper "On K_(1,k)-factorizations of a complete bipartite graph" (Discrete Math,1994, 126; 359-364), investigated the K_(1,q)-factorization of K_(m,n) and gave a sufficientcondition for such a factorization to exist. In the paper "K_(1,k)-factorizations of completebipartite graphs" (Discrete Math, 2002, 259: 301-306), Du and Wang extended Wang'sresult to the case that q is any positive integer In this paper, we give a sufficient conditionfor K_(m,n) to have a K_(p,q)-factorization. As a special case, it is shown that the Martin's BACconjecture is true when p: q=k: (k+1) for any positive integer k. 相似文献
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The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale’s channel assignment problem, which was first explored by Griggs and Yeh. For positive integerp ≥q, the λ p,q -number of graph G, denoted λ(G;p, q), is the smallest span among all integer labellings ofV(G) such that vertices at distance two receive labels which differ by at leastq and adjacent vertices receive labels which differ by at leastp. Van den Heuvel and McGuinness have proved that λ(G;p, q) ≤ (4q-2) Δ+10p+38q-24 for any planar graphG with maximum degree Δ. In this paper, we studied the upper bound of λ p ,q-number of some planar graphs. It is proved that λ(G;p, q) ≤ (2q?1)Δ + 2(2p?1) ifG is an outerplanar graph and λ(G;p,q) ≤ (2q?1) Δ + 6p - 4q - 1 if G is a Halin graph. 相似文献
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高随祥 《应用数学学报(英文版)》2001,17(1):129-139
1. IntroductionA gash G is an ordered pair of disjoillt sets (V, E) such that E is a subset of the setof unordered pairs of V, where the sets V and E are finite. The set V is cajled the setof venices and E is called the set of edges. They are usually denoted by V(G) and E(C),respectively. An edge (x, y) is said to join the venices x and y, and is sometimes denotedby xo or ear. By our definition, a graph does not colltain any loOP, neither does it colltainmultiple edges.Other terms undef… 相似文献