
It is known that there are at least 8784 non-isomorphic designs with parameters
Let
The degree sequence of a finite graph
A dice family
After introducing and discussing the notion of length two path centered surface area for general graphs, particularly for bipartite graphs, we derive a closed-form expression and an explicit expression for the length two path centered surface areas of the hypercube and the star graph, respectively.
The Ramsey numbers
A Stanton-type graph
For a nontrivial connected graph
In this paper, we consider the use of balanced arrays (B-arrays) in constructing discrete fractional factorial designs (FFD) of resolution
For integers
A difference system of sets (DSS) is any collection of subsets of
In testing web applications, details of user visits may be recorded in a web log and converted to test cases. This is called user-session-based testing and studies have shown that such tests may be effective at revealing faults. However, for popular web applications with a larger user base, many user-sessions may build up and test suite management techniques are needed. In this paper, we focus on the problem of test suite prioritization. That is, given a large test suite, reorder the test cases according to a criterion that is hypothesized to increase the rate of fault detection. Previous work shows that 2-way combinatorial-based prioritization is an effective prioritization criterion. We develop a greedy algorithm where we consider memory usage and the time that it takes to prioritize test suites. We represent software tests in a graph by storing unique parameters as vertices and
The lattice-simplex covering density problem aims to determine the minimal density by which lattice translates of the
An efficient conditional expectation algorithm for generating covering arrays has established a number of the best known upper bounds on covering array numbers. Despite its theoretical efficiency, the method requires a large amount of storage and time. In order to extend the range of its application, we generalize the method to find covering arrays that are invariant under the action of a group, reducing the search to consider only orbit representatives of interactions to be covered. At the same time, we extend the method to construct a generalization of covering arrays called quilting arrays. The extended conditional expectation algorithm, as expected, provides a technique for generating covering and quilting arrays that reduces the time and storage required. Remarkably, it also improves on the best known bounds on covering array numbers in a variety of parameter situations.
Historically, a number of problems and puzzles have been introduced that initially appeared to have no connection to graph colorings but, upon further analysis, suggested graph colorings problems. In this paper, we discuss two combinatorial problems and several graph colorings problems that are inspired by these two problems. We survey recent results and open questions in this area of research as well as some relationships among these coloring parameters and well-known colorings and labelings.
Let
A vertex
Given two disjoint copies of a graph
We show that for a connected graph
Further, we characterize permutation graphs
In a recent paper, E. Gelman provided an exact formula for the number of subgroups of a given index for the Baumslag-Solitar groups
An
For a nontrivial connected graph
All connected graphs
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