共查询到20条相似文献,搜索用时 46 毫秒
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Yong Yang 《Journal of Algebra》2009,321(7):2012-2021
Suppose V is a completely reducible faithful G-module for a solvable group G, we show G has a “large” orbit on V. Specifically, there is such that is contained in a normal subgroup of derived length 9 contained in the seventh ascending Fitting subgroup of G. This is in some ways best possible. This is applied to generate many theorems showing that a solvable group must have characters of large degree. 相似文献
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A cubic graph is -arc-transitive if acts transitively on the set of arcs of , and -basic if is -arc-transitive and has no non-trivial normal subgroup with more than two orbits. Let be a solvable group. In this paper, we first classify all connected -basic cubic graphs and determine the group structure for every . Then, combining covering techniques, we prove that a connected cubic -arc-transitive graph is either a Cayley graph, or its full automorphism group is of type , that is, a -regular group with no involution reversing an edge, and has a non-abelian normal subgroup such that the corresponding quotient graph is the complete bipartite graph of order . 相似文献
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Let and be the adjacency matrix and the degree matrix of a graph , respectively. The matrix is called the signless Laplacian matrix of . The spectrum of the matrix is called the Q-spectrum of . A graph is said to be determined by its Q-spectrum if there is no other non-isomorphic graph with the same Q-spectrum. In this paper, we prove that all starlike trees whose maximum degree exceed are determined by their Q-spectra. 相似文献
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A subgroup H of a group G is said to permute with the subgroup K of G if . Subgroups H and K are mutually permutable (totally permutable) in G if every subgroup of H permutes with K and every subgroup of K permutes with H (if every subgroup of H permutes with every subgroup of K). If H and K are mutually permutable and , then H and K are totally permutable. A subgroup H of G is S-permutable in G if H permutes with every Sylow subgroup of G. A group G is called a PST-group if S-permutability is a transitive relation in G. Let be the set of prime divisors of the order of a finite group G with the set of prime divisors of the order of the normal subgroup N of G. A set of Sylow subgroups , , form a strong Sylow system with respect to N if is a mutually permutable product for all and . We show that a finite group G is a solvable PST-group if and only if it has a normal subgroup N such that is nilpotent and G has a strong Sylow system with respect to N. It is also shown that G is a solvable PST-group if and only if G has a normal solvable PST-subgroup N and is a solvable PST-group. 相似文献
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Bangteng Xu 《Journal of Algebra》2009,321(9):2521-2539
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In this paper, we give sufficient conditions for a graph to have degree bounded trees. Let G be a connected graph and . We denote by the minimum value of the degree sum in G of any k pairwise nonadjacent vertices of A, and by the number of components of the subgraph of G induced by . Our main results are the following: (i) If , then G contains a tree T with maximum degree ⩽k and . (ii) If , then G contains a spanning tree T with for any . These are generalizations of the result by S. Win [S. Win, Existenz von Gerüsten mit Vorgeschriebenem Maximalgrad in Graphen, Abh. Math. Seminar Univ. Humburg 43 (1975) 263–267] and degree conditions are sharp. 相似文献
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John D. LaGrange 《Linear algebra and its applications》2012,436(7):1863-1871
Let A be the adjacency matrix of the zero-divisor graph of a finite commutative ring R containing nonzero zero-divisors. In this paper, it is shown that is the zero-divisor graph of a Boolean ring if and only if . Also, A is similar to plus or minus its inverse whenever R is a Boolean ring. As a consequence, it is proved that is the zero-divisor graph of a Boolean ring if and only if the set of eigenvalues (including multiplicities) of can be partitioned into 2-element subsets of the form . Furthermore, any finite Boolean ring R is characterized by the degree and coefficients of the characteristic polynomial of A. 相似文献
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For a given graph G and a positive integer r the r-path graph, , has for vertices the set of all paths of length r in G. Two vertices are adjacent when the intersection of the corresponding paths forms a path of length , and their union forms either a cycle or a path of length in G. Let be the k-iteration of r-path graph operator on a connected graph G. Let H be a subgraph of . The k-history is a subgraph of G that is induced by all edges that take part in the recursive definition of H. We present some general properties of k-histories and give a complete characterization of graphs that are k-histories of vertices of 2-path graph operator. 相似文献
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Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and the term rank of G, by and , respectively. It was conjectured [C. van Nuffelen, Amer. Math. Monthly 83 (1976) 265–266], for any graph G, . The first counterexample to this conjecture was obtained by Alon and Seymour [J. Graph Theor. 13 (1989) 523–525]. Recently, Fishkind and Kotlov [Discrete Math. 250 (2002) 253–257] have proved that for any graph G, . In this Note we improve Fishkind–Kotlov upper bound and show that . To cite this article: S. Akbari, H.-R. Fanaï, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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Let G be an LCA group, H a closed subgroup, Γ the dual group of G and μ be a regular finite non-negative Borel measure on Γ. We give some necessary and sufficient conditions for the density of the set of trigonometric polynomials on Γ with frequencies from H in the space . 相似文献
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We study vertex partitions of graphs according to their Colin de Verdiere parameter μ. By a result of Ding et al. [DOSOO] we know that any graph G with admits a vertex partition into two graphs with μ at most . Here we prove that any graph G with admits a vertex partition into three graphs with μ at most . This study is extended to other minor-monotone graph parameters like the Hadwiger number. 相似文献
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Hua Wang 《Discrete Mathematics》2008,308(15):3407-3411
The Randi? index of a graph G is the sum of over all edges of G, where denotes the degree of in G, . When , it is the weight of a graph. Delorme, Favaron, and Rautenbach characterized the trees with a given degree sequence with maximum weight, where the question of finding the tree that minimizes the weight is left open. In this note, we characterize the extremal trees with given degree sequence for the Randi? index, thus answering the same question for weight. We also provide an algorithm to construct such trees. 相似文献
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《Discrete Mathematics》2006,306(8-9):820-826
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