The phrase "a planar graph" is correct and usable in written English.
It can be used in mathematical or computer science contexts when discussing graphs that can be drawn on a plane without any edges crossing.
Example: "In graph theory, a planar graph is one that can be drawn on a flat surface without any edges intersecting."
Alternatives: "a flat graph" or "a two-dimensional graph".
A planar graph is one in which the edges have no intersection or common points except at the edges.
Paul Chew, There is a Planar Graph Almost as Good as the Complete Graph, Symposium on Computational Geometry (1986), 169-177.
K5 is not a planar graph, because there does not exist any way to connect every vertex to every other vertex with edges in the plane such that no edges intersect.
In an equivalent graph-theoretic form, one may translate this problem to ask whether the vertices of a planar graph can always be coloured by using just four colours in such a way that vertices joined by an edge have different colours.
The disk dimension of a planar graph G is the least number k for which G embeds in the plane minus k open disks, with every vertex on the boundary of some disk.
Our result implies that if the guest graph has an excluded minor of a fixed size, such as a planar graph, then we can obtain an edge-congestion of O ΔlogN) for d= 2 and O for any fixed d≥3.
The contact process proofs make use of a planar-graph duality in the graphical representation, due to Durrett and Schonmann.
A graph is called a maximal planar graph if the planarity will be not held by joining any two nonadjacent vertices of.
Finally, local planarization requires checking all the possible local forwarders in a suitable planar graph, usually a Gabriel graph.
By Corollary 2.2, is either a maximal planar graph or a.
Lu et al. [8] and Guo et al. [9] gave the upper bounds for the Laplacian spectral radius of a triangulation and a maximal planar graph, respectively.
