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
Chemistry is a fundamental science that is essential for understanding the world around us
Chemistry is the study of matter, its properties, composition, structure, and the changes that it undergoes. It is a fundamenta...
The book emphasizes the importance of practical applications
The significance of practical applications is a key theme throughout the book. It underscores the idea that learning by doing i...
Exploring trigonometry in mathematics
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fu...
Utilizing technology for personalized learning experiences
One of the most powerful tools available to learners today is technology. With the rise of the internet and mobile devices, ind...
Divideand-conquer algorithms break down problems into subproblems
One common strategy for designing algorithms to solve complex problems is the divide-and-conquer approach. This approach involv...
Trigonometric Identities and Applications
Trigonometric identities play a crucial role in simplifying trigonometric expressions and solving trigonometric equations. Thes...
Cutsets break graph disconnected components
When a graph has a cutset, it means that there is a set of vertices whose removal disconnects the graph. This concept is crucia...
Graph coloring strategies map vertices colors
One way to understand graph coloring strategies is to think of them as a way to assign colors to the vertices of a graph. Each ...