42150150
The Upper Forcing Geodetic Number of a Graph
36753167
k-Geodomination in graphs
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.
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.
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.
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 .
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.
12427163
MetaCyc: a multiorganism database of metabolic pathways and enzymes
MetaCyc is a database of metabolic pathways and enzymes located at http://MetaCyc.org/. Its goal is to serve as a metabolic encyclopedia, containing a collection of non-redundant pathways central to small molecule metabolism, which have been reported in the experimental literature. Most of the pathways in MetaCyc occur in microorganisms and plants, although animal pathways are also represented. MetaCyc contains metabolic pathways, enzymatic reactions, enzymes, chemical compounds, genes and review-level comments. Enzyme information includes substrate specificity, kinetic properties, activators, inhibitors, cofactor requirements and links to sequence and structure databases. Data are curated from the primary literature by curators with expertise in biochemistry and molecular biology. MetaCyc serves as a readily accessible comprehensive resource on microbial and plant pathways for genome analysis, basic research, education, metabolic engineering and systems biology. Querying, visualization and curation of the database is supported by SRI's Pathway Tools software. The PathoLogic component of Pathway Tools is used in conjunction with MetaCyc to predict the metabolic network of an organism from its annotated genome. SRI and the European Bioinformatics Institute employed this tool to create pathway/genome databases (PGDBs) for 165 organisms, available at the BioCyc.org website. These PGDBs also include predicted operons and pathway hole fillers.
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.
27409707
A service-based network architecture for wearable robots
We are developing a network architecture for our novel robot concept of wearable robot. Wearable robots are mobile information devices capable of supporting remote communication and intelligent interaction between networked entities. In this paper, a service-based wearable robot network architecture that involves extensions to the Jini network model is presented. We discuss three extensions to the original Jini model. The first extension involves the incorporation of a task coordinator service such that the execution of the services can be managed using a priority queue. The second extension enables the system to automatically push the required service proxy to the client intelligently based on certain system-related conditions. In the third extension, we allow the system to automatically deliver the services based on contextual information. Using a fuzzy-logic-based decision making system, the matching service can determine whether the service should be automatically delivered utilizing the information provided by the service, client, lookup service and context sensors. An application scenario has been implemented to demonstrate the feasibility of this distributed service-based robot architecture.
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.