3952660
Automorphism groups and isomorphisms of Cayley digraphs
Abstract We call a Cayley digraph X = Cay(G, S) normal for G if the right regular representation R(G) of G is normal in the full automorphism group Aut(X) of X. In this paper we give some examples of normal and nonnormal Cayley digraphs and survey some results about the normality of Cayley digraphs. We also propose some conjectures and problems about them. In the last section of this paper we discuss a problem about isomorphisms of Cayley digraphs.
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.
43124802
On the Isomorphisms of Cayley Graphs of Abelian Groups
Let G be a finite group, S a subset of G\{1}, and let Cay (G, S) denote the Cayley digraph of G with respect to S. If, for any subset T of G\{1}, Cay(G, S) ≅ Cay(G, T) implies that Sα = T for some α ∈ Aut(G), then S is called a CI-subset. The group G is called a CIM-group if for any minimal generating subset S of G, S ∪ S-1 is a CI-subset. In this paper, CIM-abelian groups are characterized.
7439709
2-Arc-transitive regular covers of complete graphs having the covering transformation group Z3p
A family of 2-arc-transitive regular covers of a complete graph is investigated. In this paper, we classify all such covering graphs satisfying the following two properties: (1) the covering transformation group is isomorphic to the elementary abelian p-group Zp3, and (2) the group of fiber-preserving automorphisms acts 2-arc-transitively. As a result, new infinite families of 2-arc-transitive graphs are constructed.
40944529
Symmetric Graphs of Order a Product of Two Distinct Primes
A simple undirected graph ? is said to be symmetric if its automorphism group Aut ? is transitive on the set of ordered pairs of adjacent vertices of ?, and ? is said to be imprimitive if Aut ? acts imprimitively on the vertices of ?. Let k and p be distinct primes with k < p. This paper gives a classification of all imprimitive symmetric graphs on kp vertices for k ? 5. The cases k < 5 have been treated previously by Cheng and Oxley (k = 2) and the second and third authors (k = 3), and the classification of primitive symmetric graphs on kp vertices with k ? 5 was done by the first and third authors.
29378412
Vertex-primitive digraphs of prime-power order are hamiltonian
Abstract Witte [6] proved that every connected Cayley digraph of a p -group is hamiltonian. In this note we generalize Witte's result to connected vertex-primitive digraphs of prime-power order; namely, we prove that every connected vertex-primitive digraph of prime-power order is hamiltonian.
227212
Exact frequency-domain reconstruction for thermoacoustic tomography. II. Cylindrical geometry
For pt. I see ibid., vol. 21, no. 7, p. 823-8 (2002). Microwave-induced thermoacoustic tomography (TAT) in a cylindrical configuration is developed to image biological tissue. Thermoacoustic signals are acquired by scanning a flat ultrasonic transducer. Using a new expansion of a spherical wave in cylindrical coordinates, we apply the Fourier and Hankel transforms to TAT and obtain an exact frequency-domain reconstruction method. The effect of discrete spatial sampling on image quality is analyzed. An aliasing-proof reconstruction method is proposed. Numerical and experimental results are included.
760808
Partial Observation vs. Blind Tracking through Occlusion
This paper presents a framework for multi-object t racking from a single fixed camera. The region-based representations of each object are tracked and p redicted using a Kalman filter. A scene model is created to help predict and interpret the occluded or exiting objects. Unlike the traditional blind tracking during occlusion, the object states are updated using partial observations whenever available. The observability of each object depends on the predictive measurement of the object, the foreground region measurement, and p erhaps the scene model. This makes the a lgorithm m ore robust i n terms of both qualitative a nd quantitative criteria.
16235334
Illumination-Invariant Motion Detection Using Colour Mixture Models
This paper tackles the problem of robust change detection in image sequences from static cameras. Motion cues are detected using frame differencing with an adaptive background estimation modelled by a mixture of Gaussians. Illumination invariance and elimination or detection of shadows is achieved by using a colour chromaticity representation of the image data. The combination of the colourand intensity-based models results in some promising applications.
15417765
The proof of a conjecture of Bouabdallah and Sotteau
Let G be a connected graph of order n. A routing in G is a set of n(n 1) fixed paths for all ordered pairs of vertices of G. The edge-forwarding index of G, (G), is the minimum of the maximum number of paths specified by a routing passing through any edge of G taken over all routings in G, and ,n is the minimum of (G) taken over all graphs of order n with maximum degree at most . To determine n 2p 1,n for 4p 2p/3 1 ≤ n ≤ 6p, A. Bouabdallah and D. Sotteau proposed the following conjecture in [On the edge forwarding index problem for small graphs, Networks 23 (1993), 249–255]. The set 3 {1, 2, . . . , (4p)/3} can be partitioned into 2p pairs plus singletons such that the set of differences of the pairs is the set 2 {1, 2, . . . , p}. This article gives a proof of this conjecture and determines that n 2p 1,n is equal to 5 if 4p 2p/3 1 ≤ n ≤ 6p and to 8 if 3p p/3 1 ≤ n ≤ 3p (3p)/5 for any p ≥ 2. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(4), 292–296 2004
441080
An efficient model for frequency-dependent on-chip inductance
this paper, we propose an ecient table-based model for frequency-dependent on-chip inductance, and apply it to com- pute mutual inductance between random wires and loop induc- tance for cascade wires, respectively. Our inductance computa- tion achieves around 5% error when compared to the numerical solution, and matches frequency-dependent impact very well. We also apply the inductance model to generate RLC circuit models for on-chip interconnects, and present a complexity- ecient normalized RLC circuit model for multiple parallel wires. These results are extremely ecient, and can be eectively used during iterative design procedure. Further, the table-based in- ductance model has been implemented as a Web-based tool to generate inductance matrix for given random wires.