20 results found for: “Apex_graph”.

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Apex graph

an apex of the graph. It is an apex, not the apex because an apex graph may have more than one apex; for example, in the minimal nonplanar graphs K5 or...

Last Update: 2023-09-04T14:45:11Z Word Count : 2785 Synonim Apex graph

Apex

peroxide Apex (geometry), the highest vertex in a polyhedron or the point where the two equal sides of an isosceles triangle meet Apex graph, a graph that...

Last Update: 2024-03-21T13:08:13Z Word Count : 783 Synonim Apex

Glossary of graph theory

triangle. apex 1.  An apex graph is a graph in which one vertex can be removed, leaving a planar subgraph. The removed vertex is called the apex. A k-apex graph...

Last Update: 2024-01-14T21:57:03Z Word Count : 15552 Synonim Glossary of graph theory

Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect...

Last Update: 2024-01-17T11:41:28Z Word Count : 4465 Synonim Planar graph

Linkless embedding

linklessly embeddable graphs have the Petersen family graphs as their forbidden minors, and include the planar graphs and apex graphs. They may be recognized...

Last Update: 2024-02-19T20:06:59Z Word Count : 3469 Synonim Linkless embedding

List of unsolved problems in mathematics

K6-minor-free graph is an apex graph Does a Moore graph with girth 5 and degree 57 exist? Do there exist infinitely many strongly regular geodetic graphs, or any...

Last Update: 2024-03-28T00:55:48Z Word Count : 19343 Synonim List of unsolved problems in mathematics

Graph minor

In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges, vertices and by contracting edges...

Last Update: 2024-01-14T19:56:27Z Word Count : 4039 Synonim Graph minor

Universal vertex

the graph of any higher-dimensional pyramid has a universal vertex as the apex of the pyramid. The trivially perfect graphs (the comparability graphs of...

Last Update: 2023-11-23T01:19:00Z Word Count : 943 Synonim Universal vertex

Wagner graph

graph. As a Möbius ladder, the Wagner graph is nonplanar but has crossing number one, making it an apex graph. It can be embedded without crossings on...

Last Update: 2024-01-27T06:32:06Z Word Count : 649 Synonim Wagner graph

Strong product of graphs

planar graphs, extensions of these results have been proven for graphs of bounded genus, graphs with a forbidden minor that is an apex graph, bounded-degree...

Last Update: 2024-01-06T03:24:51Z Word Count : 1312 Synonim Strong product of graphs

Möbius ladder

a nonplanar apex graph, meaning that it cannot be drawn without crossings in the plane but removing one vertex allows the remaining graph to be drawn...

Last Update: 2023-12-02T19:09:02Z Word Count : 1390 Synonim Möbius ladder

Treewidth

In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest...

Last Update: 2024-03-04T07:28:02Z Word Count : 4533 Synonim Treewidth

Forbidden graph characterization

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to...

Last Update: 2024-03-14T01:23:36Z Word Count : 1207 Synonim Forbidden graph characterization

Graph structure theorem

In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between...

Last Update: 2024-01-11T06:35:39Z Word Count : 2765 Synonim Graph structure theorem

Robertson–Seymour theorem

graph theory, the Robertson–Seymour theorem (also called the graph minor theorem) states that the undirected graphs, partially ordered by the graph minor...

Last Update: 2023-09-11T12:19:24Z Word Count : 2515 Synonim Robertson–Seymour theorem

Petersen family

In graph theory, the Petersen family is a set of seven undirected graphs that includes the Petersen graph and the complete graph K6. The Petersen family...

Last Update: 2024-01-06T22:27:25Z Word Count : 898 Synonim Petersen family

Cuboid

mathematical language a cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. A special case of a cuboid is a rectangular...

Last Update: 2024-03-02T22:14:54Z Word Count : 393 Synonim Cuboid

Bidimensionality

planar graphs, map graphs, bounded-genus graphs and graphs excluding any fixed minor. In particular, bidimensionality theory builds on the graph minor...

Last Update: 2024-03-18T03:09:59Z Word Count : 1390 Synonim Bidimensionality

Pyramid (geometry)

formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid...

Last Update: 2024-02-04T09:57:13Z Word Count : 1417 Synonim Pyramid (geometry)

Hadwiger number

eight-vertex Wagner graph. The graphs with Hadwiger number at most five include the apex graphs and the linklessly embeddable graphs, both of which have...

Last Update: 2023-07-02T15:50:07Z Word Count : 1221 Synonim Hadwiger number

Main result

Apex graph

In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called an apex of the graph. It is an apex, not the apex because an apex graph may have more than one apex; for example, in the minimal nonplanar graphs K5 or K3,3, every vertex is an apex. The apex graphs include graphs that are themselves planar, in which case again every vertex is an apex. The null graph is also counted as an apex graph even though it has no vertex to remove. Apex graphs are closed under the operation of taking minors and play a role in several other aspects of graph minor theory: linkless embedding, Hadwiger's conjecture, YΔY-reducible graphs, and relations between treewidth and graph diameter.


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