共查询到20条相似文献,搜索用时 468 毫秒
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John Bamberg S.P. Glasby Luke Morgan Alice C. Niemeyer 《Journal of Pure and Applied Algebra》2018,222(10):2931-2951
Let be a prime. For each maximal subgroup with , we construct a d-generator finite p-group G with the property that induces H on the Frattini quotient and . A significant feature of this construction is that is very small compared to , shedding new light upon a celebrated result of Bryant and Kovács. The groups G that we exhibit have exponent p, and of all such groups G with the desired action of H on , the construction yields groups with smallest nilpotency class, and in most cases, the smallest order. 相似文献
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Yehong Shao 《Discrete Mathematics》2018,341(12):3441-3446
Let be a graph and be its line graph. In 1969, Chartrand and Stewart proved that , where and denote the edge connectivity of and respectively. We show a similar relationship holds for the essential edge connectivity of and , written and , respectively. In this note, it is proved that if is not a complete graph and does not have a vertex of degree two, then . An immediate corollary is that for such graphs , where the vertex connectivity of the line graph
and the second iterated line graph are written as and respectively. 相似文献
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The -restricted arc connectivity of digraphs is a common generalization of the arc connectivity and the restricted arc connectivity. An arc subset of a strong digraph is a -restricted arc cut if has a strong component with order at least such that contains a connected subdigraph with order at least . The -restricted arc connectivity of a digraph is the minimum cardinality over all -restricted arc cuts of .Let be a strong digraph with order and minimum degree . In this paper, we first show that exists if and, furthermore, if , where is the minimum 3-degree of . Next, we prove that if . Finally, we give examples showing that these results are best possible in some sense. 相似文献
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Let be a weighted oriented graph with skew adjacency matrix . Then is usually referred as the weighted oriented graph associated to . Denote by the characteristic polynomial of the weighted oriented graph , which is defined asIn this paper, we begin by interpreting all the coefficients of the characteristic polynomial of an arbitrary real skew symmetric matrix in terms of its associated oriented weighted graph. Then we establish recurrences for the characteristic polynomial and deduce a formula on the matchings polynomial of an arbitrary weighted graph. In addition, some miscellaneous results concerning the number of perfect matchings and the determinant of the skew adjacency matrix of an unweighted oriented graph are given. 相似文献
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Let be a finite simple graph. For , the difference of , where is the neighborhood of and is called the critical difference of . is called a critical set if equals the critical difference and is the intersection of all critical sets. is the union of all critical independent sets. An independent set is an inclusion minimal set with if no proper subset of has positive difference.A graph is called a König–Egerváry graph if the sum of its independence number and matching number equals .In this paper, we prove a conjecture which states that for any graph the number of inclusion minimal independent set with is at least the critical difference of the graph.We also give a new short proof of the inequality .A characterization of unicyclic non-König–Egerváry graphs is also presented and a conjecture which states that for such a graph , the critical difference equals , is proved.We also make an observation about using Edmonds–Gallai Structure Theorem as a concluding remark. 相似文献
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Bao-Xuan Zhu 《Discrete Mathematics》2018,341(8):2359-2365
Given two graphs and , assume that and is a subset of . We introduce a new graph operation called the incidence product, denoted by , as follows: insert a new vertex into each edge of , then join with edges those pairs of new vertices on adjacent edges of . Finally, for every vertex , replace it by a copy of the graph
and join every new vertex being adjacent to to every vertex of . It generalizes the line graph operation. We prove that the independence polynomial where is its matching polynomial. Based on this formula, we show that the incidence product of some graphs preserves symmetry, unimodality, reality of zeros of independence polynomials. As applications, we obtain some graphs so-formed having symmetric and unimodal independence polynomials. In particular, the graph introduced by Cvetkovi?, Doob and Sachs has a symmetric and unimodal independence polynomial. 相似文献
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For a graph let , and denote its independence number, matching number, and vertex cover number, respectively. If or, equivalently, , then is a König–Egerváry graph.In this paper we give a new characterization of König–Egerváry graphs. 相似文献
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《Stochastic Processes and their Applications》2014,124(12):4202-4223
We calculate the density function of , where is the maximum over of a reflected Brownian motion , where stands for the last zero of before , , is the hitting time of the level , and is the left-hand point of the interval straddling . We also calculate explicitly the marginal density functions of and . Let and be the analogs of and respectively where the underlying process is the Lindley process, i.e. the difference between a centered real random walk and its minimum. We prove that converges weakly to as . 相似文献
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For a graph , let denote its number of vertices, its minimum degree and its cycle space. Call a graph Hamilton-generated if and only if every cycle in is a symmetric difference of some Hamilton circuits of . The main purpose of this paper is to prove: for every there exists such that for every graph with vertices,
- (1)if and is odd, then is Hamilton-generated,
- (2)if and is even, then the set of all Hamilton circuits of generates a codimension-one subspace of and the set of all circuits of having length either or generates all of ,
- (3)if and is balanced bipartite, then is Hamilton-generated.