Planar graphs embed surfaces from "summary" of Introduction to Graph Theory by Douglas Brent West
A planar graph can be drawn in such a way that no edges intersect. This means that the graph can be represented on a flat surface without any edges crossing over each other. However, sometimes a planar graph may not be able to be drawn on a flat surface without edges intersecting. In this case, the graph can still be drawn on a surface with a certain number of holes, known as a surface. The concept of planar graphs embedding surfaces refers to the ability to draw a planar graph on a surface without any edge intersections. This surface can be a sphere, a torus, or any other closed surface. The embedding of a planar graph on a surface is a way of representing the graph without any edge crossings, similar to how it would be represented on a flat surface. When a planar graph is embedded on a surface, it is important to consider the properties of the surface. For example, a graph embedded on a sphere may have different properties than a graph embedded on a torus. The surface on which the graph is embedded can affect the properties and characteristics of the graph, such as its genus or orientability. In graph theory, the concept of embedding planar graphs on surfaces is important for understanding the properties and relationships between graphs and surfaces. By studying how planar graphs can be embedded on different surfaces, researchers can gain insights into the connections between graph theory and topology. This concept allows for a deeper understanding of the relationships between graphs and surfaces, and how they can be represented and studied in different contexts.
Similar Posts
Paths sequences connected vertices
A path in a graph is a sequence of distinct vertices in which consecutive vertices are adjacent. For example, in the graph G = ...
Embracing a love of learning for lifelong success
Learning is a lifelong endeavor that holds the key to success in various aspects of life. It is not just about acquiring knowle...
Charles's law relates volume and temperature of a gas
Charles's law is a fundamental principle in chemistry that establishes a relationship between the volume and temperature of a g...
Solving problems related to time and speed calculations
Time and speed calculations are fundamental concepts in mathematics that are often used in various real-life situations. These ...
Clear explanations help demystify scientific principles
Understanding scientific principles can often be a daunting task for students, with complex theories and jargon making the subj...
Surface Area of Cylinders and Cones
Surface area is the total area that covers the surface of a three-dimensional object. For cylinders and cones, the surface area...
Graph theory important mathematics fields
Graph theory is a branch of mathematics that deals with the study of graphs, which are mathematical structures used to model pa...