17288174
The Tutte polynomial for homeomorphism classes of graphs
We study a polynomial which contains, as special cases, the Tutte polynomials of all members of a given homeomorphism class of graphs. We further show that this polynomial can be directly derived from the chain polynomial introduced in [1].
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.
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.
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.
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.
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.
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
6273632
Uniform comparison of data models using containment modeling
Containment data models are a subset of entity relationship models in which the allowed relationships are either a type of containment, storage, or inheritance. This paper describes containment relationships, and containment data models, applying them to model a broad range of monolithic, link server, and hyperbase systems, as well as the Dexter reference model, and the WWW with WebDAV extensions. A key quality of containment data models is their ability to model systems uniformly, allowing a broad range of systems to be compared consistently.
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.
14788283
Automatic Identification of Bug-Introducing Changes
Bug-fixes are widely used for predicting bugs or finding risky parts of software. However, a bug-fix does not contain information about the change that initially introduced a bug. Such bug-introducing changes can help identify important properties of software bugs such as correlated factors or causalities. For example, they reveal which developers or what kinds of source code changes introduce more bugs. In contrast to bug-fixes that are relatively easy to obtain, the extraction of bug-introducing changes is challenging. In this paper, we present algorithms to automatically and accurately identify bug-introducing changes. We remove false positives and false negatives by using annotation graphs, by ignoring non-semantic source code changes, and outlier fixes. Additionally, we validated that the fixes we used are true fixes by a manual inspection. Altogether, our algorithms can remove about 38%~51% of false positives and 14%~15% of false negatives compared to the previous algorithm. Finally, we show applications of bug-introducing changes that demonstrate their value for research