Real life situations such as travelling over time and across distance can be drawn on a graph. Exact distances and times are plotted on the graph. These are shown as co-ordinates. These points are ...

An algebraic distance graph is defined to be a graph with vertices in E n in which two vertices are adjacent if and only if the distance between them is an algebraic number. It is proved that an ...

The distance graph shows the height of a plane as it completes a journey. When the plane is at a height of 38,000 feet (ft), it travels at a constant speed of 550 miles per hour. The question asks how ...

For a given set M of positive integers, a well-known problem of Motzkin asked to determine the maximal asymptotic density of M-sets, denoted by μ(M), where an M-set is a set of non-negative integers ...

Problem: How many colors are needed so that if each point in the plane is assigned one of the colors, no two points which are exactly distance 1 apart will be assigned the same color? This problem has ...