206563147
The Geodetic Number of an Oriented Graph
For two vertices u and v of an oriented graph D, the set I(u, v) consists of all vertices lying on a u?v geodesic or v?u geodesic in D. If S is a set of vertices of D, then I(S) is the union of all sets I(u, v) for vertices u and v in S. The geodetic number g(D) is the minimum cardinality among the subsets S of V(D) with I(S) =V(D). Several results concerning the geodetic numbers of connected oriented graphs are presented. For a nontrivial connected graph G, the lower orientable geodetic number g?(G) of G is the minimum geodetic number among the orientations of G and the upper orientable geodetic number g+(G) is the maximum such geodetic number. It is shown that g?(G)?g+(G) for every connected graph of order at least 3. The lower and upper orientable geodetic numbers of several well known classes of graphs are determined. It is shown that for every two integers n and m with 1 ?n? 1 ?m? (n 2) , there exists a connected graph G of order n and size m such that g+(G) =n.
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.
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 .
207074250
Hamiltonian colorings of graphs
For vertices u and v in a connected graph G of order n, the length of a longest u-v path in G is denoted by D(u,v). A hamiltonian coloring c of G is an assignment c of colors (positive integers) to the vertices of G such that D(u,v)+|c(u)-c(v)|>=n-1 for every two distinct vertices u and v of G. The value hc(c) of a hamiltonian coloring c of G is the maximum color assigned to a vertex of G. The hamiltonian chromatic number hc(G) of G is min{hc(c)} over all hamiltonian colorings c of G. Hamiltonian chromatic numbers of some special classes of graphs are determined. It is shown that for every two integers k and n with k>=1 and n>=3, there exists a hamiltonian graph of order n with hamiltonian chromatic number k if and only if 1=
36753167
k-Geodomination in graphs
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.
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.
10549314
The Arabidopsis Information Resource (TAIR): a model organism database providing a centralized, curated gateway to Arabidopsis biology, research materials and community
Arabidopsis thaliana is the most widely-studied plant today. The concerted efforts of over 11 000 researchers and 4000 organizations around the world are generating a rich diversity and quantity of information and materials. This information is made available through a comprehensive on-line resource called the Arabidopsis Information Resource (TAIR) (http://arabidopsis.org), which is accessible via commonly used web browsers and can be searched and downloaded in a number of ways. In the last two years, efforts have been focused on increasing data content and diversity, functionally annotating genes and gene products with controlled vocabularies, and improving data retrieval, analysis and visualization tools. New information include sequence polymorphisms including alleles, germplasms and phenotypes, Gene Ontology annotations, gene families, protein information, metabolic pathways, gene expression data from microarray experiments and seed and DNA stocks. New data visualization and analysis tools include SeqViewer, which interactively displays the genome from the whole chromosome down to 10 kb of nucleotide sequence and AraCyc, a metabolic pathway database and map tool that allows overlaying expression data onto the pathway diagrams. Finally, we have recently incorporated seed and DNA stock information from the Arabidopsis Biological Resource Center (ABRC) and implemented a shopping-cart style on-line ordering system.
1895171
Data mining for selective visualization of large spatial datasets
Data mining is the process of extracting implicit, valuable, and interesting information from large sets of data. Visualization is the process of visually exploring data for pattern and trend analysis, and it is a common method of browsing spatial datasets to look for patterns. However the growing volume of spatial datasets make it difficult for humans to browse such datasets in their entirety, and data mining algorithms are needed to filter out large uninteresting parts of spatial datasets. We construct a web-based visualization software package for observing the summarization of spatial patterns and temporal trends. We also present data mining algorithms for filtering out vast parts of datasets for spatial outlier patterns. The algorithms were implemented and tested with a real-world set of Minneapolis-St. Paul (Twin Cities) traffic data.
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.