1. After a consideration of the existing data and of the sources of error involved, an arrangement of apparatus, free from these errors, is described for measuring the relative energy necessary in different portions of the spectrum in order to produce a colorless sensation in the eye. 2. Following certain reasoning, it is shown that the reciprocal of this relative energy at any wave-length is p...

In this paper we introduce unit bar k-visibility graphs, which are bar kvisibility graphs in which every bar has unit length. We show that almost all families of unit bar k-visibility graphs and unit bar k-visibility graphs are incomparable under set inclusion. In addition, we establish the largest complete graph that is a unit bar k-visibility graph. As well, we present a family of hyperbox vi...

Navigation can be studied in a graph-structured framework in which the navigating agent (which we shall assume to be a point robot) moves from node to node of a \graph space". The robot can locate itself by the presence of distinctively labeled \landmark" nodes in the graph space. For a robot navigating in Euclidean space, visual detection of a distinctive landmark provides information about th...

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

A terrain is an x-monotone polygonal line in the xy-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are...

We study a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments S in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibilit...