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 调和图
 harmonious graph
 Let C be the cycle with n vertexes0In this paper, it proved that the disjoint union of cycles C2~+1UC2(j≥1,k≥2 and (j,k)≠(1,2)) is a harmonious graph. 本文证明了对任意的j≥1，k≥2且(j，k)≠(1，2)，C_(2j+1)∪C_(2k)是调和图。 并进一步给出如下猜想： 短句来源 Harmonious Graph and Harmonious Matrix 调和图与调和矩阵 短句来源 C n+ 2 is not harmonious graph,when n≡2(mod 8),n≡4(mod 8),n≡6(mod 8); 当n为偶数且n≠ 0 (mod 8)时 ,不是调和图 . 短句来源 C n⊙Pt is not harmonious graph,when n+t≡1(mod 2). 证明了当n+t为奇数时 ,龙Cn⊙Pt不是调和图 . 短句来源 The dissertation also proves that gear graph is harmonious graph by the same strategy. 此外利用本文给出的搜索图的调和标号的限界策略,还证明了齿轮图是调和图。 短句来源 更多
 harmonic graphs
 Dress and Gutman gave an concept of harmonic graphs: The graph G is said to be harmonic if there exists a constant A, such that the equality A(G)d(G)=Ad(G) holds. Dress和Gutman从图中路数目的计算,提出了调和图的概念:一个图G称为是调和的,如果存在一个数λ,使A(G)d(G)=λd(G)。 短句来源 Pentacyclic and Hexacyclic Harmonic Graphs 五圈及六圈调和图 短句来源 Earlier all harmonic trees were determined and all unicyclic , acyclic, bicyclic, tricyclic and tetracyclic harmonic graphs were characterized. 从特征值上来看,一个非正则图G是λ-调和图当且仅当G恰以λ和0为主特征值。 具有较少圈的连通的调和图:如调和树,单圈图,双圈图,三圈图和四圈图都以完全确定。 短句来源 In my paper, we go a step further and find all pentacyclic and hexacyclic harmonic graphs: (1) : There are exactly 62 connected pentacyclic harmonic graphs, where there are exactly 56 non-regular and 5 regular connected pentacyclic 3-harmonic graphs and there exist exactly 1 non-regular connected pentacyclic 4-harmonic graphs. 本论文研究并确定了所有的五圈调和图和六圈调和图:(1):连通的五圈调和图恰有62个。 其中,连通非正则的五圈3-调和图恰有56个; 短句来源 (2) : there are exactly 77 connected hexacyclic harmonic graphs, where there are exactly 55 non-regular and 19 regular connected hexacyclic 3-harmonic graphs and there exist exactly 2 non-regular and 1 regular connected hexacyclic 4-harmonic graphs. 连通正则的六圈3-调和图恰有19个; 连通非正则的六圈4-调和图恰有2个; 短句来源
 harmonious graphs
 It′s proved that the disjoint union of cycles C 3∪C 2k (k≥3) and the disjoint unions of cycles C 5∪C 2k (k≥2) are harmonious graphs. 证明了 Seoud等当 k≥ 3时 C3 与 C2 k的不相交并 C3 ∪ C2 k为调和图的猜想 ,并扩展该结果 ,证明了 C5 ∪ C2 k( k≥ 2 )是调和图 ; 短句来源 Based on this fact the authors give a conjecture that the disjoint union of cycles C 2j+1 ∪C 2k (j≥1,k≥2 and (j,k)≠(1,2)) are harmonious graphs. 给出猜想 C2 j+ 1 ∪ C2 k( j≥ 1,k≥ 2且 ( j,k)≠ ( 1,2 ) )是调和图 . 短句来源 It′s also proved that P 4 n (8≤n≤17) and P 5 n (14≤k≤17) are harmonious graphs. 证明了幂图 P4n( 8≤ n≤ 17)与 P5 n( 14≤ n≤ 17)是调和图 ,否定了 Seoud等关于当且仅当 1≤ k≤ 3时 Pkn( 1≤ k≤ n -1)是调和图的猜想 . 短句来源 Some Results on Harmonious Graphs 关于调和图的一些结果(英文) 短句来源
 “调和图”译为未确定词的双语例句
 Harmony of graphs C_(2j+1)∪C_(2k) and graphs P_n~k C_(2j+1)∪C_(2k)类与P_n~k类调和图 短句来源 This paper constructs a class of the graph-sieve graph S(n,t),and proves that the sieve graph S(2m+1,t) is harmonious when n=2m+1. 本文构造了一个图类—团筛图S(n,t),证明了,当n=2m+1时,对任m≥1,t≥1,团筛图S(2m+1,t)都是调和图。 短句来源 This paper propored a concept of cap- tassels graph and illustrated that M(2m+ 1,t,G) is harmonious when n=2m+ 1 and G is strong harmonious. 提出了帽挂图M（n，t，G）的概念，并证明了，当n＝2m＋1，m≥1，t≥1并G为一个强调和图时M（2m＋1，t，G）是调和图的结论，同时也对M（2m，t，G）的调和性给出了评述 短句来源 This paper has studied the narmonicity of the Crown Qn(2| n) ,and given the necessary condition of the harmonicity for the Crown Qn(2|n). Thus,a kind of feasible scheme about harmonious labeling of Crown Qn (2|n) is given and proved the harmonicity of the Crown Qn (2|n ) when n=4,6,8,10,12,14,16,18. 文章研究了皇冠Qn(2|n)的调和性,给出了关于Qn(2|n)调和的必要条件,从而确定了一类可行的调和设计方案．并验证了当n=4,6,8,10,12,14,16,18时,Qn(2|n)为调和图． 短句来源 MATRIC EXPRESSIONS OF GRACEFUL GRAPH AND HARMONIC GRAPH 优美图与调和图的矩阵表示 短句来源 更多

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 This paper introduces a new concept of harmonious matrix, and demonstrates that the relation between a harmonious graph (with its labelling) and a harmonious matrix is a 1—1 correspond (theorem 1). This Paper also introduces a new concept of harmonious interlaced graph and proves that a graph is harmonious interlaced if and only if it also is interlaced (theorem 2). This paper studies the method that both harmonious interlaced graphs are pasted or linked to become a larger harmonious interlaced graph. 本文提出了调和矩阵的概念,并论述了调和图(连同其标号)与调和矩阵的一一对应关系(定理1)。本文又提出了调和交错图的概念,并证明了:一个图是调和交错的,当且仅当它又是一个交错图(定理2)。最后,本文还研究了用两个调和交错图粘成或连成一个较大的调和交错图的可能性。 This paper introduces new concepts of graceful matrix and har-monic matrix,and proves that a graph is graceful or harmonic iff there exists agraceful or harmonic matrix which is a P-adjacent matrix of a graph.This paperalso introduces a new concept of harmonic interlaced graph,and proves that agraph is interlaced iff it is also harmonic interlaced. 本文引入了优美矩阵与调和矩阵的概念,证明了一个图G是优美(调和)图,当且仅当存在一个优美(调和)矩阵A,它是G的一个P形邻接矩阵.本文又引入了调和交错图的概念,证明一个图是交错图,当且仅当它也是一个调和交错图. Since Graham R. L. and Sloan N. J. A. advanced the concept of the harmonious graph in 1980. Many such researching papers are published. This paper constructs a class of the graph-sieve graph S(n,t),and proves that the sieve graph S(2m+1,t) is harmonious when n=2m+1. 自从1980年Graham和Sloane提出调和图的概念以来,关于调和图的研究文章越来越多。本文构造了一个图类—团筛图S(n,t),证明了,当n=2m+1时,对任m≥1,t≥1,团筛图S(2m+1,t)都是调和图。 << 更多相关文摘
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