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191.
Ademir Hujdurović 《Discrete Mathematics》2019,342(9):2542-2548
A canonical double cover of a graph is the direct product of and the complete graph on two vertices. In order to answer the question when a canonical double cover of a given graph is a Cayley graph, in 1992 Maru?i? et al. introduced the concept of generalized Cayley graphs. In this paper this concept is generalized to a wider class of graphs, the so-called extended generalized Cayley graphs. It is proved that the canonical double cover of a connected non-bipartite graph is a Cayley graph if and only if is an extended generalized Cayley graph. This corrects an incorrectly stated claim in [Discrete Math. 102 (1992), 279–285]. 相似文献
192.
In (Gluskin, Litvak in Geom. Dedicate 90:45–48, [2002]) it was shown that a polytope with few vertices is far from being symmetric in the Banach–Mazur distance. More precisely,
it was shown that Banach–Mazur distance between such a polytope and any symmetric convex body is large. In this note we introduce
a new, averaging-type parameter to measure the asymmetry of polytopes. It turns out that, surprisingly, this new parameter
is still very large, in fact it satisfies the same lower bound as the Banach–Mazur distance. In a sense it shows the following
phenomenon: if a convex polytope with small number of vertices is as close to a symmetric body as it can be, then most of its vertices
are as bad as the worst one. We apply our results to provide a lower estimate on the vertex index of a symmetric convex body, which was recently introduced
in (Bezdek, Litvak in Adv. Math. 215:626–641, [2007]). Furthermore, we give the affirmative answer to a conjecture by Bezdek (Period. Math. Hung. 53:59–69, [2006]) on the quantitative illumination problem. 相似文献
193.
The node-searching problem, introduced by Kirousis and Papadimitriou, is equivalent to several important problems, such as the interval thickness problem, the path-width problem, the vertex separation problem, and so on. In this paper, we generalize the avenue concept, originally proposed for trees, to block graphs whereby we design an efficient algorithm for computing both the search numbers and optimal search strategies for block graphs. It answers the question proposed by Peng et al. of whether the node-searching problem on block graphs can be solved in polynomial time. 相似文献
194.
Victor G. Kac 《Advances in Mathematics》2008,217(6):2485-2562
We extend classical results of Kostant et al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting an analogue of Vogan's conjecture on infinitesimal characters of Harish-Chandra modules in terms of Dirac cohomology. For our calculations we use the machinery of Lie conformal and vertex algebras. 相似文献
195.
196.
Alexander Veremyev Oleg A. Prokopyev Vladimir Boginski Eduardo L. Pasiliao 《European Journal of Operational Research》2014
We consider a clique relaxation model based on the concept of relative vertex connectivity. It extends the classical definition of a k-vertex-connected subgraph by requiring that the minimum number of vertices whose removal results in a disconnected (or a trivial) graph is proportional to the size of this subgraph, rather than fixed at k. Consequently, we further generalize the proposed approach to require vertex-connectivity of a subgraph to be some function f of its size. We discuss connections of the proposed models with other clique relaxation ideas from the literature and demonstrate that our generalized framework, referred to as f-vertex-connectivity, encompasses other known vertex-connectivity-based models, such as s-bundle and k-block. We study related computational complexity issues and show that finding maximum subgraphs with relatively large vertex connectivity is NP-hard. An interesting special case that extends the R-robust 2-club model recently introduced in the literature, is also considered. In terms of solution techniques, we first develop general linear mixed integer programming (MIP) formulations. Then we describe an effective exact algorithm that iteratively solves a series of simpler MIPs, along with some enhancements, in order to obtain an optimal solution for the original problem. Finally, we perform computational experiments on several classes of random and real-life networks to demonstrate performance of the developed solution approaches and illustrate some properties of the proposed clique relaxation models. 相似文献
197.
198.
A graph G is called quasi-claw-free if for any two vertices x and y with distance two there exists a vertex u∈N(x)∩N(y) such that N[u]⊆N[x]∪N[y]. This concept is a natural extension of the classical claw-free graphs. In this paper, we present two sufficient conditions for vertex pancyclicity in quasi-claw-free graphs, namely, quasilocally connected and almost locally connected graphs. Our results include some well-known results on claw-free graphs as special cases. We also give an affirmative answer to a problem proposed by Ainouche. 相似文献
199.
František Kardoš 《Discrete Mathematics》2009,309(15):4942-4948
Let G=(V,E,F) be a 3-connected simple graph imbedded into a surface S with vertex set V, edge set E and face set F. A face α is an 〈a1,a2,…,ak〉-face if α is a k-gon and the degrees of the vertices incident with α in the cyclic order are a1,a2,…,ak. The lexicographic minimum 〈b1,b2,…,bk〉 such that α is a 〈b1,b2,…,bk〉-face is called the type of α.Let z be an integer. We consider z-oblique graphs, i.e. such graphs that the number of faces of each type is at most z. We show an upper bound for the maximum vertex degree of any z-oblique graph imbedded into a given surface. Moreover, an upper bound for the maximum face degree is presented. We also show that there are only finitely many oblique graphs imbedded into non-orientable surfaces. 相似文献
200.
王松 《数学物理学报(A辑)》2012,32(2):290-296
该文研究了秩为1的格顶点算子超代数的自同构群的一些基本性质, 并且给出了它的完全分类. 相似文献