共查询到20条相似文献,搜索用时 0 毫秒
1.
Margit Voigt 《Discrete Mathematics》2009,309(15):4926-4930
Let G=G(V,E) be a simple graph, L a list assignment with |L(v)|=Δ(G)∀v∈V and W⊆V an independent subset of the vertex set. Define to be the minimum distance between two vertices of W. In this paper it is shown that if G is 2-connected with Δ(G)=3 and G is not K4 then every precoloring of W is extendable to a proper list coloring of G provided that d(W)≥6. An example shows that the bound is sharp. This result completes the investigation of precoloring extensions for graphs with |L(v)|=Δ(G) for all v∈V where the precolored set W is an independent set. 相似文献
2.
Emre Kolotoğlu 《组合设计杂志》2013,21(11):524-530
A decomposition of a complete graph into disjoint copies of a complete bipartite graph is called a ‐design of order n. The existence problem of ‐designs has been completely solved for the graphs for , for , K2, 3 and K3, 3. In this paper, I prove that for all , if there exists a ‐design of order N, then there exists a ‐design of order n for all (mod ) and . Giving necessary direct constructions, I provide an almost complete solution for the existence problem for complete bipartite graphs with fewer than 18 edges, leaving five orders in total unsolved. 相似文献
3.
Bubble-Sort图和Modified Bubble-Sort图是两类特殊的Cayley图,由于其在网络构建中的应用而受到广泛关注.本文完全确定了这两类图的自同构群. 相似文献
4.
半二面体群的小度数Cayley图 总被引:1,自引:0,他引:1
群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在Aut X中正规.研究了4m阶半二面体群G=〈a,b a2m=b2=1,ab=am-1〉的3度和4度Cayley图的正规性,其中m=2r且r>2,并得到了几类非正规的Cayley图. 相似文献
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群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在AutX中正规.研究了4m阶拟二面体群G=a,b|a~(2m)=b~2=1,a~b=a~(m+1)的4度Cayley图的正规性,其中m=2~r,且r2,并得到拟二面体群的Cayley图的同构类型. 相似文献
9.
图的spread定义为图的邻接矩阵的最大特征值与最小特征值的差.本文确定了n(n≥84)顶点四圈图中spread最大的唯一的图. 相似文献
10.
Sanming Zhou 《Journal of Graph Theory》2014,75(1):37-47
Unitary graphs are arc‐transitive graphs with vertices the flags of Hermitian unitals and edges defined by certain elements of the underlying finite fields. They played a significant role in a recent classification of a class of arc‐transitive graphs that admit an automorphism group acting imprimitively on the vertices. In this article, we prove that all unitary graphs are connected of diameter two and girth three. Based on this, we obtain, for any prime power , a lower bound of order on the maximum number of vertices in an arc‐transitive graph of degree and diameter two. 相似文献
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Cover-Incomparability Graphs of Posets 总被引:1,自引:1,他引:0
Boštjan Brešar Manoj Changat Sandi Klavžar Matjaž Kovše Joseph Mathews Antony Mathews 《Order》2008,25(4):335-347
Cover-incomparability graphs (C-I graphs, for short) are introduced, whose edge-set is the union of edge-sets of the incomparability
and the cover graph of a poset. Posets whose C-I graphs are chordal (resp. distance-hereditary, Ptolemaic) are characterized
in terms of forbidden isometric subposets, and a general approach for studying C-I graphs is proposed. Several open problems
are also stated. 相似文献
14.
Mark S. MacLean 《Journal of Algebraic Combinatorics》2003,17(2):125-147
Let denote a bipartite distance-regular graph with diameter D 4, valency k 3, and distinct eigenvalues 0 > 1 > ··· > D. Let M denote the Bose-Mesner algebra of . For 0 i D, let E
i denote the primitive idempotent of M associated with
i
. We refer to E
0 and E
D as the trivial idempotents of M. Let E, F denote primitive idempotents of M. We say the pair E, F is taut whenever (i) E, F are nontrivial, and (ii) the entry-wise product E F is a linear combination of two distinct primitive idempotents of M. We show the pair E, F is taut if and only if there exist real scalars , such that
i + 1
i + 1 –
i – 1
i – 1 =
i
(
i + 1 –
i – 1) +
i
(
i + 1 –
i – 1) + (1 i D – 1)where 0, 1, ...,
D
and 0, 1, ...,
D
denote the cosine sequences of E, F, respectively. We define to be taut whenever has at least one taut pair of primitive idempotents but is not 2-homogeneous in the sense of Nomura and Curtin. Assume is taut and D is odd, and assume the pair E, F is taut. We show
for 1 i D – 1, where = 1, = 1. Using these equations, we recursively obtain 0, 1, ..., D and 0, 1, ...,
D
in terms of the four real scalars , , , . From this we obtain all intersection numbers of in terms of , , , . We showed in an earlier paper that the pair E
1, E
d is taut, where d = (D – 1)/2. Applying our results to this pair, we obtain the intersection numbers of in terms of k, , 1, d, where denotes the intersection number c
2. We show that if is taut and D is odd, then is an antipodal 2-cover. 相似文献
15.
图X称为边正则图,若X的自同构群Aut(X)在X的边集上的作用是正则的.本文考察了三度边正则图与四度Cayley图的关系,给出了一个由四度Cayley图构造三度边正则图的方法,并且构造了边正则图的三个无限族. 相似文献
16.
符号图$S=(S^u,\sigma)$是以$S^u$作为底图并且满足$\sigma: E(S^u)\rightarrow\{+,-\}$. 设$E^-(S)$表示$S$的负边集. 如果$S^u$是欧拉的(或者分别是子欧拉的, 欧拉的且$|E^-(S)|$是偶数, 则$S$是欧拉符号图(或者分别是子欧拉符号图, 平衡欧拉符号图). 如果存在平衡欧拉符号图$S''$使得$S''$由$S$生成, 则$S$是平衡子欧拉符号图. 符号图$S$的线图$L(S)$也是一个符号图, 使得$L(S)$的点是$S$中的边, 其中$e_ie_j$是$L(S)$中的边当且仅当$e_i$和$e_j$在$S$中相邻,并且$e_ie_j$是$L(S)$中的负边当且仅当$e_i$和$e_j$在$S$中都是负边. 本文给出了两个符号图族$S$和$S''$,它们应用于刻画平衡子欧拉符号图和平衡子欧拉符号线图. 特别地, 本文证明了符号图$S$是平衡子欧拉的当且仅当$\not\in S$, $S$的符号线图是平衡子欧拉的当且仅当$S\not\in S''$. 相似文献
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本文引进了图G(G_1,G_2,…,G_(|E(G)|))、G(G_1~(|E(G)|))的概念,此外,还引进了序优美图、可逆优美图、偶图的优美函数等概念,对于某些特殊的偶图,给出了利用小阶优美偶图构造大阶优美偶图的一种方法,由此证明了某些偶图是K-优美图。 相似文献
19.
Let Г be a G-symmetric graph admitting a nontrivial G-invariant partition
. Let Г
be the quotient graph of Г with respect to
. For each block B ∊
, the setwise stabiliser GB of B in G induces natural actions on B and on the neighbourhood Г
(B) of B in Г
. Let G(B) and G[B] be respectively the kernels of these actions. In this paper we study certain “local actions" induced by G(B) and G[B], such as the action of G[B] on B and the action of G(B) on Г
(B), and their influence on the structure of Г.
Supported by a Discovery Project Grant (DP0558677) from the Australian Research Council and a Melbourne Early Career Researcher
Grant from The University of Melbourne. 相似文献
20.
Chi-Kwong Li 《Linear and Multilinear Algebra》2013,61(7):683-693
The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two graphs are equienergetic if they have the same energy. We construct infinite families of graphs equienergetic with edge-deleted subgraphs. 相似文献