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.
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=
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.
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 .
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.
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.
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.
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.
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.