Báo cáo toán học: "Recognizing circulant graphs of prime order in polynomial time" doc

... eﬃcient.Recognizing circulant graphs of prime order in polynomial time∗Mikhail E. MuzychukNetanya Academic College42365 Netanya, Israelmikhail@netvision.net.ilGottfried TinhoferTechnical University of ... W of indices write AWfor the submatrix of A consisting of all rows and columns index with elements of W . It is easy to see by inspection thateach of the blocks Adj(A)γi(a)is of one of ... particular, circulant graphs have been studied intensively in the literature. These graphs are easily seen to be vertex transitive. In the case of a prime vertex number n circulant graphs are...

Báo cáo toán học: "Recognizing circulant graphs in polynomial time: An application of association schemes" pot

... of working with the interplay between association schemes and S-rings has beensuccessfully employed in [21] for the case of circulants on a prime number of vertices. In this paper we are going ... simple fact can be used in order to reducethe task of constructing a Cayley numbering of G to the task of ﬁnding such a numberingfor the factor graph G/τ and extending it to G.Proposition ... 05C85.Abstract In this paper we present a time -polynomial recognition algorithm for certainclasses of circulant graphs. Our approach uses coherent conﬁgurations and Schurrings generated by circulant graphs...

Báo cáo toán học: "On the Graphs of Hoﬀman-Singleton and Higman-Sims" docx

... 70 pairs of disjoint triples, 315 pairs of triples which intersect in one point, and210 pairs of triples which intersect in two points. Since the subgraph induced by L2isregular of degree ... construction of the Hoﬀman-Singleton graph from the 15 points and35 lines of PG(3, 2), where edges between points and lines indicate incidence, and edgesbetween lines indicate disjointness of their ... corresponding triples, is also evident in theproof of Lemma 43. In addition, one sees again the bijection between lines of PG(3, 2) andtriples of a 7-element set, in which intersecting lines correspond...

Báo cáo toán học: "H-free graphs of large minimum degree" doc

... one we obtain. The problem of determining the behavior of the best possible value of ρ, as well as that of deciding if the n-term can be replacedby O(1), remain open.A weaker version of Corollary ... of the vertices of G into r parts which maximizesthe number of crossing edges between the parts. Then for every x ∈ Viand j = i thenumber of neighbors of x in Viis at most the number of ... following weaker bound.the electronic journal of combinatorics 13 (2006), #R19 2all of whose vertices are typical. If there are at least s2=3r−53r−3s1typical vertices in one of the remaining...

Báo cáo toán học: "Recognizing Cluster Algebras of Finite type" doc

... the list of all minimal 2 -in nite diagrams, which are cluster alge-braic analogues of extended Dynkin graphs. 1 IntroductionCluster algebras were introduced in [4] by Fomin and Zelevinsky to ... statements in our proof of Lemma 6.1. Forthe remaining vertices they follow from a direct check.the electronic journal of combinatorics 14 (2007), #R3 21Recognizing Cluster Algebras of Finite typeAhmet ... list of Happel and Vossieck up to a natural operation of replacing the dotted edges indicatingrelations of quivers in [8] by arrows in the reverse direction. This remarkable coincidence of 1After...

Báo cáo toán học: "The maximum number of perfect matchings in graphs with a given degree sequence" docx

... permutation of rows and columns A is ablock diagonal matrix in which each block is a square all-1 matrix.Proof of Theorem 1.1: The square of the number of perfect matchings of G countsordered pairs of ... countsordered pairs of such matchings. We claim that this is the number of spanning 2-regularsubgraphs H of G consisting of even cycles (including cycles of length 2 which are thesame edge ... 2stimes, with s being the number of components (that is, cycles) of H with more than 2 vertices. Indeed, every union of apair of perfect matchings M1, M2is a 2-regular spanning subgraph H as...

Báo cáo toán học: " On the boundedness of the solutions in nonlinear discrete Volterra difference equations" pot

... non-decreasing mapping such that φ(v) > 0, v > 0, andφ(0) = 0 where . is any ﬁxed norm on Rd. In recent years, there has been an increasing interest in the study of the asymptotic behavior of ... boundedness of the solutions of linear Volterra diﬀerence equations, we refer thereaders to [10–12]. We give some applications of our main result for sub-linear, linear, and super-linearVolterra ... below).For information about publishing your research in Advances in Difference Equations go tohttp://www.advancesindifferenceequations.com/authors/instructions/For information about other SpringerOpen...

Báo cáo toán học: " Analysis and modeling of spatial characteristics in urban microscenario of heterogeneous network" potx

... intra-cellinterference, while the interference from the othersites is defined as inter-cell interference. The ratio of the intra-site interference to inter-site interference isdefined asR =IintraIinter(14)From ... is 4 × 2 in downlink.For intra-site CoMP, the joint processing with blockdiagonalization algorithm is adopted [19] since thedownlink CSI can be obtained at the eNB by upl inksounding. The ... distribution.To find the mean angle de noted in Figure 6, i.e., thecenter of all paths in one cycle, the coordinate system in which the angle spread is minimized need to bedetermined. Offset values...

Báo cáo toán học: " Criteria for robustness of heteroclinic cycles in neural microcircuits" potx

... Discussion In this article, we have introduced a testable criterion for robustness for a given cycle of heteroclinic con-nections within constrained settings—this test involves finding the connection ... nonlinearfunction that represents both the intrinsic firing and that due to interaction with the other cells in thenetwork. These systems have a very rich set of invariant subspaces because of ... consider constraints in the system. For this case, it is natural to investigate theinvariance of a set of affine subspaces of the system’s phase space related to the type of synaptic couplingconsidered....

Báo cáo toán học: "Improving Dense Packings of Equal Disks in a Square" ppsx

... journal of combinatorics (2000),#R46 5are n ≤ 27, and these proofs involve substantial computation as the value of n increases,and the examination of an exponentially increasing number of cases.Before ... be conﬁrmed by using suﬃcient accuracy in approximatingthe appropriate root of P (x1) = 0. As is typical in this type of variable elimination, caremust be taken in deciding just how it is ... obstaclerepels in the direction from the point of local minimum of the distance to the center of a.)• The length of a repelling vector is dα,whereα is a preselected parameter, and d = d1if the repelling...

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