206570343
Vertex-Primitive Graphs of Order a Product of Two Distinct Primes
Abstract Let k and p be odd primes with k p . All vertex-primitive graphs of order kp are classified, and those which are symmetric, or are edge-transitive but not symmetric. or are not Cayley graphs are identified. In addition, a classification is given of all vertex-primitive, edge-transitive lantisymmetric) directed graphs or order kp . The classification of the vertex-primitive symmetric graphs of order kp is used by the authors and others to complete the classification of symmetric graphs or order kp . The classification of the vertex-primitive non-Cayley graphs of order kp is used by B.D. McKay and the first author in an investigation of vertex-transitive non-Cayley graphs.
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.
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.
39351233
Note on Infinite Families of Trivalent Semisymmetric Graphs
A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. This paper uses the groups PSL (2, p) and PGL (2, p), where p is a prime, to construct two new infinite families of trivalent semisymmetric graphs.
1797921
Arc-transitive circulant digraphs of odd prime-power order
In this paper, the full automorphism group of a circulant digraph of prime-power order is investigated, and as a result, a complete classification of arc-transitive circulant graphs of odd prime-power order is given.
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
872168
The super connectivity of shuffle-cubes
The shuffle-cube SQn, where n ≡ 2 (mod 4), a new variation of hypercubes proposed by Li et al. [T.-K. Li, J.J.M. Tan, L.-H. Hsu, T.-Y. Sung, The shuffle-cubes and their generalization, Inform. Process. Lett. 77 (2001) 35-41], is an n-regular n-connected graph. This paper determines that the super connectivity of SQn is 2n - 4 and the super edge-connectivity is 2n - 2 for n ≥ 6.
502799
Multifacet's general execution-driven multiprocessor simulator (GEMS) toolset
The Wisconsin Multifacet Project has created a simulation toolset to characterize and evaluate the performance of multiprocessor hardware systems commonly used as database and web servers. We leverage an existing full-system functional simulation infrastructure (Simics [14]) as the basis around which to build a set of timing simulator modules for modeling the timing of the memory system and microprocessors. This simulator infrastructure enables us to run architectural experiments using a suite of scaled-down commercial workloads [3]. To enable other researchers to more easily perform such research, we have released these timing simulator modules as the Multifacet General Execution-driven Multiprocessor Simulator (GEMS) Toolset, release 1.0, under GNU GPL [9].
10735574
Forwarding indices of folded n-cubes
For a given connected graph G of order n, a routing R is a set of n(n - 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forwarding index of a graph is the maximum number of paths of R passing through any vertex (resp. edge) in the graph. In this paper, the authors determine the vertex and the edge forwarding indices of a folded n-cube as (n-1)2n-1 +1-((n+l)/2) (n ⌊n+1/2⌋) and 2n-(n,⌊n+1/2⌋),respectively.
53245552
Simultaneous shield insertion and net ordering for capacitive and inductive coupling minimization
In this article, we first show that existing net ordering formulations to minimize noise are no longer sufficient with the presence of inductive noise, and shield insertion is needed to minimize inductive noise. Using a Keff model as the figure of merit for inductive coupling, we then formulate two simultaneous shield insertion and net ordering (SINO) problems: the optimal SINO/NF problem to find a minimal area SINO solution that is free of capacitive and inductive noise, and the optimal SINO/NB problem to find a minimal area SINO solution that is free of capacitive noise and is under the given inductive noise bound. We reveal that both optimal SINO problems are NP-hard, and propose effective approximate algorithms for the two problems. Experiments show that our SINO/NB algorithm uses from 51p to 82p fewer shields compared to uniform shield insertion and net ordering (US + NO), and uses from 4p to 47p fewer shields compared to separated net ordering and shield insertion (NO + SI). Furthermore, the SINO/NB solutions under practical noise bounds use from 38p to 61p fewer shields compared to SINO/NF solutions, and use up to 36p fewer shields compared to the theoretical lower bound for optimal SINO/NF solutions. Moreover, we show that the Keff model has a high fidelity versus the noise voltage computed using accurate RLC circuit models and SPICE simulations. To the best of our knowledge, it is the first work that presents an in-depth study on the automatic layout optimization of multiple nets to minimize both capacitive and inductive noise.