OUTERPLANAR Meaning and
Definition
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Outerplanar is an adjective used to describe a graph or a drawing in graph theory. A graph, in this context, refers to a collection of vertices, or points, that are connected by edges, or lines. An outerplanar graph, specifically, is a graph that can be represented in a plane without any of its edges crossing each other, except at their endpoints.
To further explain, an outerplanar graph can be visualized as a set of points arranged in the plane in such a way that the edges connecting the points never intersect, except at their endpoints. This means that the graph can be drawn on a two-dimensional plane without any of its edges crossing over one another. In other words, the graph can be embedded in a plane.
The term "outerplanar" originates from the idea that the graph's drawing does not contain any edges in its inner region, only along its outer boundary or periphery. As a result, outerplanar graphs are often perceived as simpler and less complex than graphs that cannot be drawn in a plane without edge crossings.
In conclusion, an outerplanar graph is a type of graph that can be visually represented on a plane without any of its edges crossing except at their endpoints. It is a concept commonly studied in the branch of mathematics known as graph theory.
Etymology of OUTERPLANAR
The word "outerplanar" is derived from a combination of two elements: "outer" and "planar".
- "Outer" comes from the Middle English term "outre", which means "outside" or "exterior". This word can be traced back to the Old English word "ūtera".
- "Planar" is derived from the Latin word "planus", which means "flat" or "level". It is also related to the Greek word "πλάνη" ("plane"), which conveys a similar meaning.
When these two elements are combined, "outerplanar" describes something that pertains to the outside or exterior of a plane or flat surface. In mathematics, it refers to objects or graphs that can be drawn in a plane in such a way that none of their edges intersect except at their endpoints, making it a planar graph with all vertices on the outer face.
