The arrangement graph was proposed as a generalization of the star graph topology. In this paper we investigate the topological properties of the (n, k)-arrangement graph &k. It has been shown that the (n, n 2)arrangement graph An,+2 is isomorphic to the n-alternating group graph AGn In addition, the exact value of average distance of A,,& has been derived.

Electron microscopy has already given much information about the macromolecular components of striated muscle (1, 4). Thus it is shown that myofibrils of teased muscle are ribbons composed of parallel arrays of filaments associated with an amount of seemingly amorphous material that is great,est in the anisotropic regions. For the present work, strips of psoas muscle separated from a rabbit at ...

Richard Stanley suggested the problem of finding the characteristic polynomial of a certain hyperplane arrangement defined by xi + xj = 0, 1, which is called the Shi threshold arrangement. We present the answer of the problem, using the finite field method.

We revisit the d-dimensional arrangement problem and analyze the performance ratios of previously proposed algorithms based on the linear arrangement problem with d-dimensional cost. The two problems are related via space-filling curves and recursive balanced bipartitioning. We prove that the worst-case ratio of the optimum solutions of these problems is Θ(log n), where n is the number of verti...

We provide a link between topological graph theory and pseudoline arrangements from the theory of oriented matroids. We investigate and generalize a function f that assigns to each simple pseudoline arrangement with an even number of elements a pair of complete-graph embeddings on a surface. Each element of the pair keeps the information of the oriented matroid we started with. We call a simple...

A generalized configuration is a set of n points and (n 2 ) pseudolines such that each pseudoline passes through exactly two points, two pseudolines intersect exactly once, and no three pseudolines are concurrent. Following the approach of allowable sequences we prove a recursive inequality for the number of (≤ k)-sets for generalized configurations. As a consequence we improve the previously b...