20403548
The chromatic uniqueness of W10
Abstract Xu and Li proved the chromatic uniqueness of wheels on an odd number of vertices. It is known that the wheels on six vertices and eight vertices are not chromatically unique. Read found that the wheel on ten vertices is chromatically unique by computer computations. Here, we sketch a mathematical proof of the chromatic uniqueness of the wheel on ten vertices.
205877725
Chromaticity of a family of K4 homeomorphs
Abstract A K 4 homeomorph can be described as a graph on n vertices having 4 vertices of degree 3 and n − 4 vertices of degree 2; each pair of degree 3 vertices is joined by a path. We study the chromatic uniqueness and chromatic equivalence of one family of K 4 homeomorphs. This family has exactly 3 paths of length one. The results of this study leads us to solve 3 of the problems posed by Koh and Teo in their 1990 survey paper which appeared in Graphs and Combinatorics.
6916623
Chromatic polynomials of generalized trees
Abstract This paper is a survey of results on chromatic polynomials of graphs which are generalizations of trees. In particular, chromatic polynomials of q -trees will be discussed. The smallest q -tree ( q ≥1) is the complete graph K q on q vertices. A q -tree on n +1 vertices where n ≥ q , is obtained by adding a new vertex adjacent to each of q arbitrarily selected, mutually adjacent vertices in a q -tree on n vertices. Another generalization of trees is the n -gon-trees. The smallest n -gon-tree ( n ≥3) is the n -gon which is a cycle of n vertices. A n -gon-tree with k +1 n -gons is obtained from a n -gon-tree with k n -gons by adding a new n -gon which has exactly one edge in common with any n -gon of a n -gon-tree with k n -gons.
911709
Homeomorphs and amallamorphs of the Petersen graph
Let P be the Petersen graph. The main results of this paper are the discovery of infinite families of chromatically equivalent pairs of P homeomorphs and the discovery of infinite families of flow equivalent pairs of P amallamorphs. In particular, three families of P homeomorphs with 8 parameters, five families with 7 parameters and many families with fewer parameters are obtained. Also one family of P amallamorphs with 9 parameters, three families with 7 parameters, seven families with 6 parameters and many families with fewer parameters are obtained.
9513339
Chromatic polynomials of homeomorphism classes of graphs
Abstract We study a multilinear polynomial which subsumes the chromatic polynomials of all the graphs in a given homeomorphism class. We show that this polynomial can be extended to include further families of homeomorphic graphs, and derive some properties of its coefficients. We also prove similar results for the dual concept of graphs with multiple edges.
5345896
Properties of academic paper references
We propose a new method to find related papers using an input paper and its hyperlinked citation relationships rather than keywords. Such related papers are especially useful as background reading for researchers new to a research field. In this paper we introduce the background reading paper extractor (BPE), and show various properties of academic paper references.
18003710
Bug Classification Using Program Slicing Metrics
In this paper, we introduce 13 program slicing metrics for C language programs. These metrics use program slice information to measure the size, complexity, coupling, and cohesion properties of programs. Compared with traditional code metrics based on code statements or code structure, program slicing metrics involve measures for program behaviors. To evaluate the program slicing metrics, we compare them with the Understand for C++ suite of metrics, a set of widely-used traditional code metrics, in a series of bug classification experiments. We used the program slicing and the Understand for C++ metrics computed for 887 revisions of the Apache HTTP project and 76 revisions of the Latex2rtf project to classify source code files or functions as either buggy or bug-free. We then compared their classification prediction accuracy. Program slicing metrics have slightly better performance than the Understand for C++ metrics in classifying buggy/bug-free source code. Program slicing metrics have an overall 82.6% (Apache) and 92% (Latex2rtf) accuracy at the file level, better than the Understand for C++ metrics with an overall 80.4% (Apache) and 88% (Latex2rtf) accuracy. The experiments illustrate that the program slicing metrics have at least the same bug classification performance as the Understand for C++ metrics.
2542573
Control choices and network effects in hypertext systems
When the utility of a hypertext system depends on the number of users and amount of data in the system, the system exhibits network effects. This paper examines how the core differences in control assumptions between monolithic hypertext systems, open hypermedia systems, and the Web, lead to different incentive structures for readers and content providers and hence varying levels of
9355668
The WebDAV property design
This paper provides a detailed description of the general design space for metadata storage capabilities. The design space considers issues of metadata identification, typing and representation, dynamic behavior, predefined and user-defined metadata, schema discovery/update, operations, API packaging/marshalling, searching, and versioning. The design space is used to structure a retrospective analysis of the three major alternative metadata designs considered during the design of the WebDAV distributed authoring protocol. Deployment experience with WebDAV properties is also discussed, with the most successful use occurring in custom client/server pairs and in protocol extensions.
12803302
Properties of Signature Change Patterns
Understanding function signature change properties and evolution patterns is important for researchers concerned with alleviating signature change impacts, understanding software evolution, and predicting future evolution patterns. We provide detailed signature change properties by analyzing seven software project histories to reveal multiple properties of signature changes, including their kind, frequency, correlation with other changes, number of parameter changes, and evolution patterns of signature change kinds. We show that signature changes can be used as measurement aid for software evolution analysis