26886692
On the geodetic number of a graph
For two vertices u and v of a graph G, the set I(u, v) consists of all vertices lying on some u − v geodesic in G. If S is a set of vertices of G, then I(S) is the union of all sets I(u, v) for u, v ∈ S. The geodetic number g(G) is the minimum cardinality among the subsets S of V(G) with I(S) = V(G). It is shown that if G is a graph of order n and diameter d then g(G) ≤ n − d + 1 and this bound is sharp. For positive integers r, d, and k ≥ 2 with r ≤ d ≤ 2r, there exists a connected graph G of radius r, diameter d, and g(G) = k. Also, for integers n, d, and k with 2 ≤ d < n, 2 ≤ k < n, and n − d − k + 1 ≥ 0, there exists a graph G of order n, diameter d, and g(G) = k. It is shown, for every nontrivial connected graph G, that g(G) ≤ g(G × K2). A sufficient condition for the equality of g(G) and g(G × K2) is presented. A graph F is a minimum geodetic subgraph if there exists a graph G containing F as an induced subgraph such that V(F) is a minimum geodetic set for G. Minimum geodetic subgraphs are characterized. © 2002 John Wiley & Sons, Inc.
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=
35168758
Detour Domination 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.
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.
6107762
Re-examining IT Enabled Change with a New Model of the Information Field: The Tiger Creek Case
This paper demonstrates the application of a new model of the information field (I-model) (Zhang & Benjamin 2006) to deconstructing case studies in the information field so that they can be easily analyzed, understood and compared. The expense tracking system at Tiger Creek case (Zuboff & Bronsema 1984) is selected owing to it beings historically important in illustrating various issues brought by informated change (Zuboff 1989), and changes in the traditional command and control process (Benjamin & Levinson 1993). Our re-examination of the case using the I-model highlights the dynamics and complex issues resulted when access to information modifies the power relationships in organizations that seem ever present in IT implementations. It also sheds new insight on research in IT-enabled change. We conclude that the I-model can provide a framework for analyzing other cases in the information field
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.
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.
1522370
A two factor theory for Website design
This study was designed to verify whether an analogy to Herzberg's hygiene-motivational theory about workplace could be used in the Web environment. According to this analogy, the presence of hygiene factors would provide the basic functionality of a Web site, while their absence would create user dissatisfaction. Motivating factors are those that contribute to user satisfaction. They add additional value and may entice users to keep returning to a Web site. In Phase I, we identified 44 core features in the Web environment that were classified into 12 categories by subjects. In Phase II, a different group of subjects in a pilot study were asked to distinguish between the hygiene and motivational characteristics of these features and categories. The preliminary results show that 4 categories and 14 features were judged to be primarily motivational, while 3 categories and 13 features were perceived to be primarily hygiene in nature. The remaining 5 categories and 17 features were perceived to be both.