10480954
Isomorphisms of Finite Cayley Digraphs of Bounded Valency
LetGbe a finite group,Sa subset ofG\{1}, and let Cay(G,S) denote the Cayley digraph ofGwith respect toS. If, for all subsetsS,TofG\{1} of size at mostm, Cay(G,S)?Cay(G,T) implies thatS?=Tfor some??Aut(G), thenGis called anm-DCI-group. In this paper, we prove that, form?2, allm-DCI-groups are of the formU×V, where (|U|, |V|)=1,Uis abelian andVbelongs to an explicitly determined list of groups. Moreover Sylow subgroups of such groups satisfy some very restrictive conditions.
206571122
On Half-Transitive Metacirculant Graphs of Prime-Power Order
In this paper, infinitely many graphs of large valency which are half-transitive (that is vertex- and edge-transitive but not arc-transitive) are constructed, and a complete classification is given of half-transitive metacirculant graphs of order a p-power and valency less than 2p, where p is a prime. In particular, it is shown that, for any odd prime p, integers n?3 and k?2 such that k divides p?1, there are exactly (pn?2?1)/2+pn?3?1 nonisomorphic connected half-transitive metacirculants of order pn and valency 2k.
27555290
Constructing Homogeneous Factorisations of Complete Graphs and Digraphs
Abstract. A homogeneous factorisation of a complete graph Kn is a partition of the edge set that is invariant under a subgroup G of Sn such that G is transitive on the parts of the partition and induces a vertex-transitive automorphism group on the graph corresponding to each part. A product construction is given for such factorisations.
23350440
On Isomorphisms of Connected Cayley Graphs, II
A Cayley graph or digraph Cay(G, S) of a finite groupGis called aCI-graphofGif, for anyT?G, Cay(G, S)?Cay(G, T) if and only ifS?=Tfor some??Aut(G). We study the problem of determining which Cayley graphs and digraphs for a given group are CI-graphs. A finite groupGis called aconnected m-DCI-group(orconnected m-CI-group) if all connected Cayley digraphs (or connected Cayley graphs, respectively) ofGof (out)-valency at most m are CI-graphs. For a groupG, letp(G) be the smallest prime divisor of |G|. It was previously shown that all finite groupsGare connected (p(G)?1)-DCI-groups and all finite groupsGare connected 2(p(G)?1)-CI-groups. In this paper, for every primep, we construct infinitely many finite groupsGsuch thatp(G)=pandGis neither a connectedp-DCI-group nor a connected 2p-CI-group, which provides solutions for several open problems in this area.
16649809
Relative difference sets fixed by inversion and Cayley graphs
Using graph theoretical technique, we present a construction of a (30, 2, 29, 14)-relative difference set fixed by inversion in the smallest finite simple group--the alternating group A5. To our knowledge this is the first example known of relative difference sets in the finite simple groups with a non-trivial forbidden subgroup. A connection is then established between some relative difference sets fixed by inversion and certain antipodal distance-regular Cayley graphs. With the connection, several families of antipodal distance-regular Cayley graphs which are coverings of complete graphs are presented.
35890566
On Isomorphisms of Minimal Cayley Graphs and Digraphs
Abstract. A Cayley graph or digraph Cay(G,S) is called a CI-graph of G if, for any T⊂G, Cay(G,S)≅Cay(G,T) if and only if Sσ=T for some σ∈Aut(G). The aim of this paper is to characterize finite abelian groups for which all minimal Cayley graphs and digraphs are CI-graphs.
46337154
Minimum cross entropy thresholding
Abstract The threshold selection problem is solved by minimizing the cross entropy between the image and its segmented version. The cross entropy is formulated in a pixel-to-pixel basis between the two images and a computationally attractive algorithm employing the histogram is developed. Without making a priori assumptions about the population distribution, this method provides an unbiased estimate of a binarized version of the image in an information theoretic sense.
17566608
Porosity of mutually nearest and mutually furthest points in Banach spaces
Let X be a real strictly convex and Kadec Banach space and G a nonempty closed relatively boundedly weakly compact subset of X. Let B(X) (resp. K(X)) be the family of nonempty bounded closed (resp. compact) subsets of X endowed with the Hausdorff distance and let BG(X) denote the closure of the set {A ∈ B(X) : A ∩ G = φ} and KG(X) = BG(X)∩K(X). We introduce the admissible family A of B(X) and prove that EAo(G) (resp. EoA(G)), the set of all subsets F ∈ A ⊆ BG(X) (resp. F ∈ A ⊆ BG(X)) such that the minimization problem min(F, G) (resp. the maximization problem max(F, G)) is well-posed, is a dense Gδ-subset of A. Furthermore, when X is uniformly convex, we prove that A\EAo(G) and A\EoA(G) are σ-porous in A.
81526
Capability based mediation in TSIMMIS
Conventional mediators focus their attention on the contents of the sources and their relationship to the integrated views provided to the users. They do not take into account the capabilities of sources to answer queries. This may lead them to generate plans involving source queries that cannot be answered by the sources. In the TSIMMIS system, we have developed a source capability sensitive plan generation module that constructs feasible plans for user queries in the presence of limited source capabilities
2028079
Strong uniqueness of the restricted Chebyshev center with respect to an RS-set in a Banach space
Let G be a strict RS-set (resp. an RS-set) in X and let F be a bounded (resp. totally bounded) subset of X satisfying rG (F) < rx (F), where rG (F) is the restricted Chebyshev radius of F with respect to G. It is shown that the restricted Chebyshev center of F with respect to G is strongly unique in the case when X is a real Banach space, and that, under some additional convexity assumptions, the restricted Chebyshev center of F with respect to G is strongly unique of order α ≥ 2 in the case when X is a complex Banach space.
3813961
Using MMQ Model for Performance Simulation of Storage Area Network
The infrastructures of SANs are complex, and the implementations/designs of SANs are varied. So finding a proper modeling method to analysis and simulate SAN performance in a systemic/consistent way is very important for the work efficiency of SAN designers and performance tuners. This paper proposes a methodology of using a multi-tier multiserver queue (MMQ) network system to model a SAN system, which can be generalized to different SAN instances neatly, and be used for both performance analysis and simulation. Besides the main idea and high-level MMQ model, the application of this method is illustrated by constructing a software simulator, which is also designed and implemented in a systemic and reusable style. The simulation validation shows that maximum error range is less than 10%. So we can consider this method a sound solution for the quick performance design comparison and analysis of SAN.