We construct orthogonal double covers of Kn,n by Pm+1 ∪∗ Sn−m, where n and m are integers, 2 ≤ m ≤ 10, m ≤ n and Pm+1 ∪∗ Sn−m is a tree obtained from the path Pm+1 with m edges and a star Sn−m with n − m edges by identifying an end-vertex of Pm+1 with the center of Sn−m.

In a recent paper [9], the authors introduced the extended Q-bipartite double of an almost dual bipartite cometric association scheme. Since the association schemes arising from linked systems of symmetric designs are almost dual bipartite, this gives rise to a new infinite family of 4-class cometric schemes which are both Q-bipartite and Q-antipodal. These schemes, the schemes arising from lin...

This paper deals with weighted set systems (V, E , q), where V is a set of indices, E ⊂ 2 and the weight q is a nonnegative integer function on E . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V, E , q) is...

A new approach is presented for computing the interior medial axes of generic regions in R bounded by C-smooth parametric B-spline surfaces. The generic structure of the 3D medial axis is a set of smooth surfaces along with a singular set consisting of edge curves, branch curves, fin points and six junction points. In this work, the medial axis singular set is first computed directly from the B...

This article indicates another set-theoretic formula, solely in terms of union and intersection, for the set limits any given sequence (net, general) an arbitrary T 1 space; this representation particular gives a new characterization space.

A bipartite graph G = (U, V,E) is convex if the vertices in V can be linearly ordered such that for each vertex u ∈ U , the neighbors of u are consecutive in the ordering of V . An induced matching H of G is a matching such that no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and m weighted edges, an induced matching of maxim...

Biclustering is a vital data mining tool which is commonly employed on microarray data sets for analysis task in bioinformat ics research and medical applications. There has been extensive research on biclustering of gene expression data arising from microarray experiment. This technique is an important analysis tool in gene expression measurement, when some genes have multip le functions and e...

The independent assignment problem (or the weighted matroid intersection problem) is extended using Dress-Wenzel’s matroid valuations, which are attached to the vertex set of the underlying bipartite graph as an additional weighting. Specifically, the problem considered is: Given a bipartite graph G = (V , V −;A) with arc weight w : A → R and matroid valuations ω and ω− on V + and V − respectiv...