20073710
On a class of Hamiltonian laceable 3-regular graphs
Abstract Using the concept of brick-products, Alspach and Zhang showed in Alspach and Zhang (1989) that all cubic Cayley graphs over dihedral groups are Hamiltonian. It is also conjectured that all brick-products C(2n, m, r) are Hamiltonian laceable, in the sense that any two vertices at odd distance apart can be joined by a Hamiltonian path. In this paper, we shall study the Hamiltonian laceability of brick-products C(2n, m, r) with only one cycle (i.e. m = 1). To be more specific, we shall provide a technique with which we can show that when the chord length r is 3, 5, 7 or 9, the corresponding brick-products are Hamiltonian laceable. Let s = gcd((r + 1)/2, n) and t = gcd((r − 1)/2, n). We then show that the brick-product C(2n, 1, r) is Hamiltonian laceable if (i) st is even; (ii) s is odd and rs  r + 1 + 3s (mod 4n); or (iii) t is odd and rt  r − 1 − 3t (mod 4n). In general, when n is sufficiently large, say n ⩾ r2 − r + 1, then the brick-product is also Hamiltonian laceable.
19946044
On edge-Hamiltonian property of Cayley graphs
Abstract Let G be a group generated by X . A Cayley graph over G is defined as a graph G ( X ) whose vertex set is G and whose edge set consists of all unordered pairs [ a,b ] with a , b ϵ G and a -1 b ϵ X ∩ X -1 , where X -1 denotes the set { x -1 ∣ x ϵ X }. When X is a minimal generating set or each element of X is of even order, it can be shown that G ( X ) is Hamiltonian if it is edge-Hamiltonian. Hence every Cayley graph of order a power of 2 is edge-Hamiltonian.
18457324
On the higher-order edge toughness of a graph
For an integer c, 1?c??V(G)??1, we define the cth-order edge toughness of a graph G as tc(G)=min|X|?(G?X)?cX?E(G) & ?(G?X)>c The objective of this paper is to study this generalized concept of edge toughness. Besides giving the of the cth-order edge toughness ?c(G) of a graph G, we prove that `?c(G)?k if and only if G has k edge-disjoint spanning forests with exactly c components?. We also study the `balancity? of a graph G of order p and size q, which is defined as the smallest positive integer c such that ?c(G) = p/(p?c).
45076304
Spatial Semantic Virtual Worlds: The Structural Duality and Beyond
2867815
Matchings and matching extensions in graphs
Abstract Let G be a graph with a perfect matching and k be an integer such that 1 ⩽ k vbV ( G ) vb /2. Then G is said to be k -extendable if every matching of size k in G extends to a perfect matching of G . Plummer (1994) proved that every (2 k + 1)-connected K 1,3 -free graph of even order is k -extendable. In this paper, it was proved that every (2 k + n − 2)-connected K 1, n -free graph of even order is k -extendable. Also, an answer to the problem of characterizing maximal k -extendable graphs posted by Plummer (1994) and Saito (1989/90) is given. Besides, we show that a regular graph of even order belongs to the first class if its any two odd cycles have at least a vertex in common.
9048744
Web-based simulation experiments
The use of the World Wide Web and Java-based mobile code provides new opportunities for distributed simulation. First, the infrastructure provided by the Internet eliminates the need for multiprocessor hardware, making it feasible to distribute simulation models over different hardware platforms through the Internet. Second, "Internet-aware" mobile Java code makes the applications fully portable and reusable. These enabling technologies are already exploited for distributed simulation modeling. This paper reports on the preliminary results of an on-going effort to construct a parallel discrete event simulation support system to distribute simulation experiments over the Internet with a view on simulation optimization. A research prototype for ranking and selection problems is described. The overall project goals are discussed.
198001
Proper interval graphs and the guard problem
This paper is a study of the hamiltonicity of proper interval graphs with applications to the guard problem in spiral polygons. We prove that proper interval graphs with ?2 vertices have hamiltonian paths, those with ?3 vertices have hamiltonian cycles, and those with ?4 vertices are hamiltonian-connected if and only if they are, respectively, 1-, 2-, or 3-connected. We also study the guard problem in spiral polygons by connecting the class of nontrivial connected proper interval graphs with the class of stick-intersection graphs of spiral polygons.
14818835
An empirical evaluation of several methods to select the best system
Simulation is an important tool for comparing the performance of several alternative systems. There is therefore significant interest in procedures that efficiently select the best system, where best is defined by the maximum or minimum expected simulation output. In this paper, we examine both two-stage and sequential procedures that represent three structurally different modeling methodologies for allocating simulation replications to identify the best system, and we evaluate them empirically with respect to several measures of effectiveness. Empirical evidence suggests that sequential procedures perform better than their two-stage counterparts, including a heuristic sequential variation on Rinott's procedure. Further, there appears to be significant benefit to using procedures based on a Bayesian, average-case analysis as opposed to the statistically-conservative indifference-zone formulation.