29718077
Greedy F-colorings of graphs
Let G=(V,E) be a connected graph. For a symmetric, integer-valued function @d on VxV, where K is an integer constant, N"0 is the set of nonnegative integers, and Z is the set of integers, we define a C-mapping F:VxVxN"0->Z by F(u,v,m)[email protected](u,v)+m-K. A coloring c of G is an F-coloring if F(u,v,|c(u)-c(v)|)>=0 for every two distinct vertices u and v of G. The maximum color assigned by c to a vertex of G is the value of c, and the F-chromatic number F(G) is the minimum value among all F-colorings of G. For an ordering s:v"1,v"2,...,v"n of the vertices of G, a greedy F-coloring c of s is defined by (1) c(v"1)=1 and (2) for each i with 1==0, for each j with 1=
6793819
Convexity in oriented graphs
For vertices u and v in an oriented graph D, the closed interval I[u,v] consists of u and v together with all vertices lying in a u−v geodesic or v−u geodesic in D. For S⊆V(D), I[S] is the union of all closed intervals I[u,v] with u,v∈S. A set S is convex if I[S]=S. The convexity number con(D) is the maximum cardinality of a proper convex set of V(D). The nontrivial connected oriented graphs of order n with convexity number n−1 are characterized. It is shown that there is no connected oriented graph of order at least 4 with convexity number 2 and that every pair k, n of integers with 1⩽k⩽n−1 and k≠2 is realizable as the convexity number and order, respectively, of some connected oriented graph. For a nontrivial connected graph G, the lower orientable convexity number con−(G) is the minimum convexity number among all orientations of G and the upper orientable convexity number con+(G) is the maximum such convexity number. It is shown that con+(G)=n−1 for every graph G of order n⩾2. The lower orientable convexity numbers of some well-known graphs are determined, with special attention given to outerplanar graphs.
37962125
On the planarity of iterated jump graphs
Abstract For a graph G of size m⩾1 and edge-induced subgraphs F and H of size r ( 1⩽r⩽m ), the subgraph H is said to be obtained from F by an edge jump if there exist four distinct vertices u,v,w, and x in G such that uv∈E(F) , wx∈E(G)−E(F) , and H=F−uv+wx . The minimum number of edge jumps required to transform F into H is the jump distance from F to H . For a graph G of size m⩾1 and an integer r with 1⩽r⩽m , the r -jump graph J r (G) is that graph whose vertices correspond to the edge-induced subgraphs of size r of G and where two vertices of J r (G) are adjacent if and only if the jump distance between the corresponding subgraphs is 1. For k⩾2 and r⩾1 , the k th iterated r -jump graph J r k (G) is defined as J r (J r k−1 (G)) , where J r 1 (G)=J r (G) . An infinite sequence {G i } of graphs is planar if every graph G i is planar. All graphs G for which {J r k (G)} ( r=1,2 ) is planar are determined and it is shown that if the sequence {J r k (G)} is nonplanar, then lim k→∞ gen( J r k (G))=∞ , where gen (G) denotes the genus of a graph G .
33626535
The Convexity Number of a Graph
Abstract. For two vertices u and v of a connected graph G, the set I[u,v] consists of all those vertices lying on a u−v shortest path in G, while for a set S of vertices of G, the set I[S] is the union of all sets I[u,v] for u,v∈S. A set S is convex if I[S]=S. The convexity number con(G) of G is the maximum cardinality of a proper convex set of G. The clique number ω(G) is the maximum cardinality of a clique in G. If G is a connected graph of order n that is not complete, then n≥3 and 2≤ω(G)≤con(G)≤n−1. It is shown that for every triple l,k,n of integers with n≥3 and 2≤l≤k≤n−1, there exists a noncomplete connected graph G of order n with ω(G)=l and con(G)=k. Other results on convex numbers are also presented.
36753167
k-Geodomination in graphs
33291432
Graphs of order n with locating-chromatic number n-1
For a coloring c of a connected graph G, let Π = (C1, C2, ..., Ck) be an ordered partition of V(G) into the resulting color classes. For a vertex v of G, the color code cΠ(v) of v is the ordered k-tuple (d(v, C1), d(v, C2),..., d(v, Ck)), where d(v, Ci) = min{d(v, x): x ∈ Ci} for 1 ≤ i ≤ k. If distinct vertices have distinct color codes, then c is called a locating-coloring. The locating-chromatic number χL(G) is the minimum number of colors in a locating-coloring of G. It is shown that if G is a connected graph of order n ≥ 3 containing an induced complete multipartite subgraph of order n - 1, then (n + 1)/2 ≤ χL(G) ≤ n and, furthermore, for each integer k with (n + 1)/2 ≤ k ≤ n, there exists such a graph G of order n with χL(G) = k. Graphs of order n containing an induced complete multipartite subgraph of order n - 1 are used to characterize all connected graphs of order n ≥ 4 with locating-chromatic number n - 1.
2843157
Expectations and rankings of Web site quality features: results of two studies on user perceptions
In the emerging electronic environment, the creation of customer-centered Web sites is becoming increasingly important. We report on two exploratory studies on user perceptions of using Web sites. We first use Kano's (1984) Model of Quality to conduct an investigation of quality features in the Web environment. An independently conducted study later expands the first study by addressing several limitations. The results of both studies suggest that: the Kano quality model can be used as a framework to control Web site quality in terms of three quality types and the time transition of the quality nature; not every feature is regarded as equally important within a Web domain; and different domains have different rankings of important features, although there are certain features that are regarded as highly important among domains studied. These studies provide some empirical evidence on user perceptions of Web site quality features and lead to further theoretical investigations.
6799021
Task-based interaction with an integrated multilingual, multimedia information system: a formative evaluation
This paper describes a formative evaluation of an integrated multilingual, multimedia information system, a series of user studies designed to guide system development. The system includes automatic speech recognition for English, Chinese, and Arabic, automatic translation from Chinese and Arabic into English, and query-based and profile-based search options. The study design emphasizes repeated evaluation with the same (increasingly experienced) participants, exploration of alternative task designs, rich qualitative and quantitative data collection, and rapid analysis to provide the timely feedback needed to support iterative and responsive development. Results indicate that users presented with materials in a language that they do not know can generate remarkably useful work products, but that integration of transcription, translation, search and profile management poses challenges that would be less evident were each technology to be evaluated in isolation.
7862760
Tagged Probe Interval Graphs
A generalization of interval graph is introduced for cosmid contig mapping of DNA. A graph is a tagged probe interval graph if its vertex set can be partitioned into two subsets of probes and nonprobes, and a closed interval can be assigned to each vertex such that two vertices are adjacent if and only if at least one of them is a probe and one end of its corresponding interval is contained in the interval corresponding to the other vertex. We show that tagged probe interval graphs are weakly triangulated graphs, hence are perfect graphs. For a tagged probe interval graph with a given partition, we give a chordal completion that is consistent to any interval completions with respect to the same vertex partition.
41611208
A Unified Approach to Detecting Spatial Outliers
Spatial outliers represent locations which are significantly different from their neighborhoods even though they may not be significantly different from the entire population. Identification of spatial outliers can lead to the discovery of unexpected, interesting, and implicit knowledge, such as local instability. In this paper, we first provide a general definition of S-outliers for spatial outliers. This definition subsumes the traditional definitions of spatial outliers. Second, we characterize the computation structure of spatial outlier detection methods and present scalable algorithms. Third, we provide a cost model of the proposed algorithms. Finally, we experimentally evaluate our algorithms using a Minneapolis-St. Paul (Twin Cities) traffic data set.
23937565
MetaCyc: a multiorganism database of metabolic pathways and enzymes
The MetaCyc database (see URL http://MetaCyc.org) is a collection of metabolic pathways and enzymes from a wide variety of organisms, primarily microorganisms and plants. The goal of MetaCyc is to contain a representative sample of each experimentally elucidated pathway, and thereby to catalog the universe of metabolism. MetaCyc also describes reactions, chemical compounds and genes. Many of the pathways and enzymes in MetaCyc contain extensive information, including comments and literature citations. SRI's Pathway Tools software supports querying, visualization and curation of MetaCyc. With its wide breadth and depth of metabolic information, MetaCyc is a valuable resource for a variety of applications. MetaCyc is the reference database of pathways and enzymes that is used in conjunction with SRI's metabolic pathway prediction program to create Pathway/Genome Databases that can be augmented with curation from the scientific literature and published on the world wide web. MetaCyc also serves as a readily accessible comprehensive resource on microbial and plant pathways for genome analysis, basic research, education, metabolic engineering and systems biology. In the past 2 years the data content and the Pathway Tools software used to query, visualize and edit MetaCyc have been expanded significantly. These enhancements are described in this paper.