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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.
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 .
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]
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 ...
Möbius–Kantor graph, in graph theory, a symmetric bipartite cubic graph with 16 vertices and 24 edges; Möbius plane, a particular kind of plane geometry, built upon some affine planes by adding one point; Möbius ladder, a cubic circulant graph
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
Notice that the number of ladders is not changed and each node's ladder remains the same. Although a node v can be listed in multiple paths now but its ladder is the one that was associated to v in the first stage of the algorithm. These two stages can be processed in O(n) time but the query time is not constant yet. Consider a level ancestor ...
Richard Kenneth Guy (30 September 1916 – 9 March 2020) was a British mathematician. He was a professor in the Department of Mathematics at the University of Calgary. [1] He is known for his work in number theory, geometry, recreational mathematics, combinatorics, and graph theory.