45692912
Triangle-Free Graphs with Large Degree
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.
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.
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).
204988011
A class of additive multiplicative graph functions
For a fixed graph G, the capacity function for G, Po, is defined by Pc(H)= lim,__,®[yo(H')] TM, where y6(H) is the maximum number of disjoint G's in H. In [2], Hsu proved that Pr2 can be viewed as a lower bound for multiplicative increasing graph functions. But it was not known whether Pr2 is multiplicative or not. In this paper, we prove that Pc is multiplicative and additive for some graphs G which include K2. Some properties of Pc are also discussed in this paper.
14147651
Understanding the evolution of NSAID: a knowledge domain visualization approach to evidence-based medicine
Finding the most rigorous, updated, and well received clinical evidence is a crucial and challenging task in the practice of evidence-based medicine (EBM). In this article, we describe a knowledge domain visualization-based quantitative approach that is designed to support the task of searching for high-quality clinical evidence in the medical literature. We illustrate the use of this new approach with the knowledge domain of non-steroidal anti-inflammatory drugs (NSAIDs). A sample of the literature is visualized in a base map depicting structural and temporal properties of emerging themes and references made by such themes over time. In addition, the visualization highlights the rigorousness of a published clinical trial in terms of the type of study design retrieved dynamically from PubMed. The contribution of this approach is that it offers users an integrated search environment so that the rigorousness, recentness, and consensus of clinical evidence can be assessed with the support of visual exploration facilities.
61982690
Fitting the jigsaw of citation: information visualization in domain analysis
Domain visualization is one of the new research fronts resulted from the proliferation of information visualization, aiming to reveal the essence of a knowledge domain. Information visualization plays an integral role in modeling and representing intellectual structures associated with scientific disciplines. In this article, the domain of computer graphics is visualized based on author cocitation patterns derived from an 18-year span of the prestigious IEEE Computer Graphics and Applications (1982-1999). This domain visualization utilizes a series of visualization and animation techniques, including author cocitation maps, citation time lines, animation of a high-dimensional specialty space, and institutional profiles. This approach not only augments traditional domain analysis and the understanding of scientific disciplines, but also produces a persistent and shared knowledge space for researchers to keep track the development of knowledge more effectively. The results of the domain visualization are discussed and triangulated in a broader context of the computer graphics field.
35624108
Optimal Parallel Routing in Star Graphs
Star graphs have been recently proposed as attractive alternatives to the popular hypercube for interconnecting processors on a parallel computer. In this paper, we present an efficient algorithm that constructs an optimal parallel routing in star graphs. Our result improves previous results for the problem.
15011824
Nearly Optimal One-to-Many Parallel Routing in Star Networks
Star networks were proposed recently as an attractive alternative to the well-known hypercube models for interconnection networks. Extensive research has been performed that shows that star networks are as versatile as hypercubes. This paper is an effort in the same direction. Based on the well-known paradigms, we study the one-to-many parallel routing problem on star networks and develop an improved routing algorithm that finds n-1 node-disjoint paths between one node and a set of other n-1 nodes in the n-star network. These parallel paths are proven of minimum length within a small additive constant, and the running time of our algorithm is bounded by O(n/sup 2/). More specifically, given a node s and n-1 other nodes {t/sub 1/, t/sub 2/, ..., t/sub n-1/} in the n-star network, our algorithm constructs n-1 node-disjoint paths P/sub 1/, P/sub 2/, ..., P/sub n-1/, where P/sub i/ is a path from s to t/sub j/ of length at most dist(s, t/sub j/)+6 and dist(s, t/sub j/) is the distance, i.e., the length of a shortest path, from s to t/sub j/, for i=1, 2, ..., n-1.The best bound on the path length by previously known algorithms for the same problem is 5(n-2)/spl ap/10/spl Delta//sub n//3, where /spl Delta//sub n/=max{dist(s, t)} is the diameter of the n-star network.