The trees, respectively unicyclic graphs, on n vertices with the smallest Laplacian permanent are studied. In this paper, by edge-grafting transformations, the n-vertex trees of given bipartition having the second and third smallest Laplacian permanent are identified. Similarly, the n-vertex bipartite unicyclic graphs of given bipartition having the first, second and third smallest Laplacian pe...

In this paper we propose and analyze a new spatial access method, namely the S∗-tree, for the efficient secondary memory encoding and manipulation of images containing multiple non-overlapping features (i.e., coloured images). We show that the S∗-tree is more space efficient than its precursor, namely the S-tree, which was explicitly designed for binary images, and whose straightforward extensi...

In this paper, we study the parameterized complexity of the problems of partitioning the vertex set of a graph into two parts VA and VB such that VA induces a graph with degree at most a (resp., an a-regular graph) and VB induces a graph with degree at most b (resp., a b-regular graph). These two problems are called Upper-Degree-Bounded Bipartition and Regular Bipartition respectively. First, w...

Let G be a bipartite graph, and let H be a bipartite graph with a fixed bipartition (BH ,WH). We consider three different, natural ways of forbidding H as an induced subgraph in G. First, G is H-free if it does not contain H as an induced subgraph. Second, G is strongly H-free if G is H-free or else has no bipartition (BG,WG) with BH ⊆ BG and WH ⊆ WG. Third, G is weakly H-free if G is H-free or...

sulfur (s) is an essential macronutrient influencing plant growth, nutrient efficiency, quality and health of agricultural crops. the purpose of this research was to study the effects of s rates and sources on growth and fruit quality of apple (malus domestica l.) trees of ‘golden delicious’ at west azerbaijan, iran. experiment was conducted during four seasons (2003-2007), using a factorial ra...

OBJECTIVE Sleeve gastrectomy is the fastest growing surgical procedure to treat obesity in the world but it may cause or worsen gastroesophageal reflux disease. This article originally aimed to describe the addition of anti-reflux procedures (removal of periesophageal fats pads, hiatoplasty, a small plication and fixation of the gastric remnant in position) to the usual sleeve gastrectomy and t...

We studied the importance of proper model assumption in the context of Bayesian phylogenetics by examining >5,000 Bayesian analyses and six nested models of nucleotide substitution. Model misspecification can strongly bias bipartition posterior probability estimates. These biases were most pronounced when rate heterogeneity was ignored. The type of bias seen at a particular bipartition appeared...

We present eecient parallel algorithms for some geometric clustering and partitioning problems. Our algorithms run in the CREW PRAM model of parallel computation. Given a point set P of n points in two dimensions, the clustering problems are to nd a k-point subset such that some measure for this subset is minimized. We consider the problems of nding a k-point subset with minimum L 1 perimeter a...

A geometric graph is a graph whose vertices are points in the plane and whose edges are straight-line segments between the points. A plane spanning tree in a geometric graph is a spanning tree that is non-crossing. Let R and B be two disjoint sets of points in the plane where the points of R are colored red and the points of B are colored blue, and let n = |R ∪ B|. A bichromatic plane spanning ...