29638112
The Steiner number of a graph
Abstract For a connected graph G of order n⩾3 and a set W⊆V(G) , a tree T contained in G is a Steiner tree with respect to W if T is a tree of minimum order with W⊆V(T) . The set S(W) consists of all vertices in G that lie on some Steiner tree with respect to W . The set W is a Steiner set for G if S(W)=V(G) . The minimum cardinality among the Steiner sets of G is the Steiner number s(G) . Connected graphs of order n with Steiner number n , n−1 , or 2 are characterized. It is shown that every pair k,n of integers with 2⩽k⩽n is realizable as the Steiner number and order of some connected graph. For positive integers r,d, and k⩾2 with r⩽d⩽2r , there exists a connected graph of radius r , diameter d , and Steiner number k . Also, for integers n,d, and k with 2⩽d , 2⩽k , and n−d−k+1⩾0 , there exists a graph G of order n , diameter d , and Steiner number k . For two vertices u and v of a connected graph G , the set I[u,v] consists of all vertices lying on some u – v geodesic in G . For U⊆V(G) , the set I[U] is the union of all sets I[u,v] for u,v∈U . A set U is a geodetic set if I[U]=V(G) . The cardinality of a minimum geodetic set is the geodetic number g(G) . It is shown that g(G)⩽s(G) and that for every two integers a and b such that 3⩽a⩽b , there exists a graph G of radius r and diameter d such that d=r+1 , g(G)=a , and s(G)=b .
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
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 .
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.
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.
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.
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.
5702445
The role of moderating factors in user technology acceptance
Along with increasing investments in new technologies, user technology acceptance becomes a frequently studied topic in the information systems discipline. The last two decades have seen user acceptance models being proposed, tested, refined, extended and unified. These models have contributed to our understanding of user technology acceptance factors and their relationships. Yet they have also presented two limitations: the relatively low explanatory power and inconsistent influences of the factors across studies. Several researchers have recently started to examine the potential moderating effects that may overcome these limitations. However, studies in this direction are far from being conclusive. This study attempts to provide a systematic analysis of the explanatory and situational limitations of existing technology acceptance studies. Ten moderating factors are identified and categorized into three groups: organizational factors, technological factors and individual factors. An integrative model is subsequently established, followed by corresponding propositions pertaining to the moderating factors.
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.