What is the graph of a sphere?
A sphere is the graph of an equation of the form x2 + y2 + z2 = p2 for some real number p. The radius of the sphere is p (see the figure below). Ellipsoids are the graphs of equations of the form ax2 + by2 + cz2 = p2, where a, b, and c are all positive.
Are planar graphs connected?
Every maximal planar graph is a least 3-connected. If a maximal planar graph has v vertices with v > 2, then it has precisely 3v – 6 edges and 2v – 4 faces.
What is a simple planar graph?
A graph G = (V,E) is planar if it can be “drawn” on the plane without edges crossing except at endpoints – a planar embedding or plane graph.
What is a k33 graph?
The graph K3,3 is called the utility graph. This usage comes from a standard mathematical puzzle in which three utilities must each be connected to three buildings; it is impossible to solve without crossings due to the nonplanarity of K3,3.
What is the center of a sphere called?
A great circle of a sphere is the intersection of a plane that contains the center of the sphere with the sphere. Its diameter is called an axis and the endpoint of the axes are called poles. (Think of the north and south poles on a globe of the earth.) A meridian of a sphere is any part of a great circle.
Can a disconnected graph be planar?
First of all there is no relation between concept of planarity & concept of connected & disconnected graph. Given disconnected graph, you can not call it either planar or non planar.
What is Kuratowski second graph?
A Kuratowski graph of the second type is the complete graph spanned by the vertices of a tetrahedron and a point in its interior. A graph G is planar (cf. Graph, planar) if and only if it does not contain a Kuratowski graph of the first or second type (the Kuratowski–Pontryagin theorem).
What is Kuratowski first graph?
Kuratowski’s first graph: A complete graph with 5 vertices is called Kuratowski’s first graph. The graph is generally denoted by K5. A regular connected graph with 6 vertices and 9 edges is called Kuratowski’s second graph. The graph is generally denoted by K3,3.
What is the intersection of a sphere and a plane?
A circle of a sphere is a circle that lies on a sphere. Such a circle can be formed as the intersection of a sphere and a plane, or of two spheres. A circle on a sphere whose plane passes through the center of the sphere is called a great circle; otherwise it is a small circle.
What is the intersection of a plane and a sphere through its center?
Great Circles A great circle is the intersection a plane and a sphere where the plane also passes through the center of the sphere. Lines of longitude and the equator of the Earth are examples of great circles.
What is meant by disconnected graph?
A graph is said to be disconnected if it is not connected, i.e., if there exist two nodes in such that no path in has those nodes as endpoints.