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In graph theory, the Möbius ladder M n, for even numbers n, is formed from an n-cycle by adding edges (called "rungs") connecting opposite pairs of vertices in the cycle. It is a cubic, circulant graph, so-named because (with the exception of M 6 (the utility graph K 3,3), M n has exactly n/2 four-cycles [1] which link together by their shared edges to form a topological Möbius strip.
Möbius ladders play an important role in the theory of graph minors.The earliest result of this type is a 1937 theorem of Klaus Wagner (part of a cluster of results known as Wagner's theorem) that graphs with no K 5 minor can be formed by using clique-sum operations to combine planar graphs and the Möbius ladder M 8. [4]
In the mathematical field of graph theory, the ladder graph L n is a planar, undirected graph with 2n vertices and 3n – 2 edges. [ 1 ] The ladder graph can be obtained as the Cartesian product of two path graphs , one of which has only one edge: L n ,1 = P n × P 2 .
The edges and vertices of these six regions form Tietze's graph, which is a dual graph on this surface for the six-vertex complete graph but cannot be drawn without crossings on a plane. Another family of graphs that can be embedded on the Möbius strip, but not on the plane, are the Möbius ladders , the boundaries of subdivisions of the ...
Mobius, also known as the Anti-Monitor, a supervillain in DC Comics; Moebius, the main antagonistic faction of Xenoblade Chronicles 3; Mobius, or Dr. Ignatio Mobius, a character in the Command & Conquer series; Moebius the Timestreamer, a character in the Legacy of Kain series; Mobius 1, the call sign of the main character of Ace Combat 04 ...
The Wagner graph, an eight-vertex Möbius ladder arising in Wagner's characterization of K 5-free graphs.. Wagner is known for his contributions to graph theory and particularly the theory of graph minors, graphs that can be formed from a larger graph by contracting and removing edges.
In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz Friedrich Tietze, who showed in 1910 that the Möbius strip can be subdivided into six regions that all touch each other – three along the boundary of the strip and three along its center line – and therefore that graphs that are embedded ...
The Möbius–Kantor graph derives its name from being the Levi graph of the Möbius–Kantor configuration. It has one vertex per point and one vertex per triple, with an edge connecting two vertices if they correspond to a point and to a triple that contains that point.