![]() ![]() And when you get down to 3 decimal points, you can get better equipment and measure down to 4 decimal points, etc, etc. The subject of graph theory had its beginnings in recreational math problems (see number game), but it has grown into a significant area of mathematical research, with applications in chemistry, operations research, social sciences, and computer science. How many hours go by until it is 64.652 degrees? Obviously, 4.652 hours, right? This function is continuous because you can break down both temperature and time into the finest increments that you can measure. graph theory, branch of mathematics concerned with networks of points connected by lines. The temperature will increase by 1 degree per hour this morning until noon. Despite the fact that you can measure a basketball players height to very small units (essentially continuous, just requiring better and better measuring equipment), shoe size is available (in the US) in 1/2 sizes (size 10, 10 1/2, 11, 11 1/2, 12, etc). The height of basketball players is roughly linear to their shoe size. So you can spend $2 and get 2 liters, $4 and get 4 liters, etc, but you cannot pay $3.82 to purchase 3.82 liters. Although the unit cost $1 per liter, it is not possible to purchase soda in any other increment than 2 liter bottles. Hodge theory on graphs develops discrete versions of the differential forms found in the continuous theory and enables a graph decomposition into gradient. Soda is on sale for $2 for a 2 liter bottle but that is the only size they have available. In other words, it is a graph with only vertices and no connections between them. The number of people is discrete meaning you bring 1, 2, 3, 4, etc to the movies. A graph of order n and size zero is a graph where there are only isolated vertices with no edges connecting any pair of vertices.A null graph is a graph with no edges. But it is not possible to take 0.2 people to the movie. How many people get to see the movie? If continuous, it would be 3.2 people. If the function were continuous, then we could say it takes 1.5 buses but there is no such thing as half a bus (at least it couldn't be driven to school. The history of graph theory may be specifically. The answer, of course is 2 buses because buses are discrete. graph theory, branch of mathematics concerned with networks of points connected by lines. Discrete means separate points that you cannot break into "in between" points.Įxample: There are 36 students how must ride the school bus. ![]()
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