A look at cycles containing specified elements of a graph

AbstractThis article is intended as a brief survey of problems and results dealing with cycles containing specified elements of a graph. It is hoped that this will help researchers in the area to identify problems and areas of concentration

Forbidden triples and traceability: a characterization

AbstractGiven a connected graph G, a family F of connected graphs is called a forbidden family if no induced subgraph of G is isomorphic to any graph in F. If this is the case, G is said to be F-free. In earlier papers the authors identified four distinct families of triples of subgraphs that imply traceability when they are forbidden in sufficiently large graphs. In this paper the authors introduce a fifth family and show these are all such families

An iterative approach to graph irregularity strength

AbstractAn assignment of positive integer weights to the edges of a simple graph G is called irregular if the weighted degrees of the vertices are all different. The irregularity strength, s(G), is the maximal edge weight, minimized over all irregular assignments, and is set to infinity if no such assignment is possible. In this paper, we take an iterative approach to calculating the irregularity strength of a graph. In particular, we develop a new algorithm that determines the exact value s(T) for trees T in which every two vertices of degree not equal to two are at distance at least eight

Application of diffracto sight ot the nondestructive inspection of aircraft structures

The D Sight optical set up was first assembled nearly ten years ago at Diffracto Ltd. It has received several patents, the first of which was in the United States [1]. Since the mid 1980’s, D Sight has been successfully applied to surface quality inspections, particularly in the automotive and plastics industries. Recently, Komorowski et al. [2–5] have shown several potential applications of D Sight in the field of nondestructive inspection of aircraft structures. The technique has been shown to be particularly effective in locating nonvisible impact damage on large surfaces of aircraft structures built from composite materials. The early work at the IAR, NRCC led to a development program for a D Sight based device for impact damage location. In parallel, new potential applications for D Sight have been identified

Gaps in the Saturation Spectrum of Trees

A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from the complement of G to G results in a copy of H. The minimum number of edges (the size) of an H-saturated graph on n vertices is denoted sat(n, H), while the maximum size is the well studied extremal number, ex(n, H). The saturation spectrum for a graph H is the set of sizes of H-saturated graphs between sat(n, H) and ex(n, H). In this paper we show that paths, trees with a vertex adjacent to many leaves, and brooms have a gap in the saturation spectrum

Near-Field Microlensing and Its Effects on Stellar Transit Observations by Kepler

In this paper, we explore the astrophysical implications of near-field microlensing and its effects on stellar transit observations, with a special emphasis on the Kepler mission. Kepler is a NASA-approved mission whose goal is to detect a large number of extrasolar, earth-like planets by obtaining near-continuous photometry of > 100,000 F, G, and K dwarfs for four years. The expected photometric precision of Kepler is 90 micromag (achieved in 15 minute samples), at which the effect of microlensing by a transiting companion can be significant. For example, for a solar-type primary transited by a white-dwarf secondary, the maximum depth of the transit is 0.01%, which is almost entirely compensated by the microlensing amplification when the white dwarf is at ~0.05 AU. The combined effect of microlensing and transit increases to a net amplification of 150 micromag at an orbital separation of 0.1 AU, and 2.4 millimag at an orbital separation of 1 AU. Thus, the effect of microlensing can be used to break the degeneracy between a planetary-mass object for which the microlensing effect is negligible, and a more massive object of the same size. For brown dwarfs at orbital separations of a few AU, the effect of microlensing is several percent of the transit depth, and hence the microlensing effect must be taken into account in deriving the physical parameters of the brown dwarf. The microlensing signal caused by a neutron star or a black hole in a binary can be several millimag, far exceeding the transit depth, and potentially detectable even from ground-based observations. Kepler will be sensitive to white dwarfs, neutron stars, and black holes in binaries through their microlensing signatures. These observations can be used to derive the frequency of such compact objects in binaries, and to determine their masses.Comment: 34 pages, including 15 figures, Accepted for publication in Astrophysical Journa