Directed edge path graphs are the intersection graphs of directed paths in a directed tree, viewed as sets of edges. They were studied by Monma and Wei (J. Comb. Theory B 41 (1986) 141–181) who also gave a polynomial time recognition algorithm. In this work, we show that the clique graphs of these graphs are exactly the two sections of the same kind of path families, and give a polynomial time ...

Longest edge refinement algorithms were designed to deal with the iterative and local refinement of triangulations for finite element applications. In 3-dimensions the algorithm locally refines a tetredra set Sref and some neighboring tetraedra in each iteration. The new points introduced in the mesh are midpoints of the longest edge of some tetrahedra of either of the input mesh or of some ref...

We give a simpler proof of the result of Boros and Füredi that for any finite set of points in the plane in general position there is a point lying in 2/9 of all the triangles determined by these points. Introduction Every set P of n points in R in general position determines ( n d+1 ) d-simplices. Let p be another point in R. Let C(P, p) be the number of the simplices containing p. Boros and F...

Four different vector fields on (x,y)-plane A vector field on a sphere ♣ Curves. A smooth curve is a continuous curve (no gaps or discontinuities) with no corners (no abrupt changes in slope at a point such as you would get from the intersection of two lines). A continuous and differentiable produces a smooth function. A path C is called closed if its initial and final points are the same point...

If φ : L → L′ is a bijection from the set of lines of a linear space (P,L) onto the set of lines of a linear space (P ′,L′) (dim (P,L), dim (P ′,L′) ≥ 3), such that intersecting lines go over to intersecting lines in both directions, then φ is arising from a collineation of (P,L) onto (P ′,L′) or a collineation of (P,L) onto the dual linear space of (P ′,L′). However, the second possibility can...

A method of representing transformations of a finite set pictorially is described. These pictures of a function are used to count certain idempotent transformations, and interesting formulae for the Fibonacci numbers are obtained. No part of any string extends beyond the region ° : : ; z ::; 1, and if two strings intersect then they join together, from the point of intersection, to meet the sam...

Ecological edges are increasingly recognized as drivers of landscape patterns and ecosystem processes. In fragmented and patchy landscapes (e.g., a fragmented forest or a savanna with scattered termite mounds), edges can become so numerous that their effects pervade the entire landscape. Results of recent studies in such landscapes show that edge effects can be altered by the presence or proxim...

an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

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...

We propose a real-time computer vision system that enables a UGV to safely cross urban road-intersections. Specifically, when the UGV approaches the stop sign at a 4-way intersection, it must be aware of the vehicles at the other three roads and adhere to traffic rules by waiting for its turn to proceed. The proposed solution consists of three main components: a vehicle detector, a tracker, and...