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Klein Graphs
In the mathematical field of graph theory, the Klein graphs are two different but related regular graphs, each with 84 edges. Each can be embedded in the orientable surface of genus 3, in which they form dual graphs. The cubic Klein graph This is a 3- regular (cubic) graph with 56 vertices and 84 edges, named after Felix Klein. It is Hamiltonian, has chromatic number 3, chromatic index 3, radius 6, diameter 6 and girth 7. It is also a 3- vertex-connected and a 3- edge-connected graph. It has book thickness 3 and queue number 2. It can be embedded in the genus-3 orientable surface (which can be represented as the Klein quartic), where it forms the Klein map with 24 heptagonal faces, Schläfli symbol 8. According to the ''Foster census'', the Klein graph, referenced as F056B, is the only cubic symmetric graph on 56 vertices which is not bipartite. It can be derived from the 28-vertex Coxeter graph. Algebraic properties The automorphism group of the Klein graph is the g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triple Torus Illustration
Triple is used in several contexts to mean "threefold" or a " treble": Sports * Triple (baseball), a three-base hit * A basketball three-point field goal * A figure skating jump with three rotations * In bowling terms, three strikes in a row * In cycling, a crankset with three chainrings Places * Triple Islands, an uninhabited island group in Nunavut, Canada * Triple Island, British Columbia, Canada * Triple Falls (other), four waterfalls in the United States & Canada * Triple Glaciers, in Grand Teton National Park, Wyoming * Triple Crossing, Richmond, Virginia, believed to be the only place in North America where three Class I railroads cross * Triple Bridge, a stone arch bridge in Ljubljana, Slovenia Transportation * Kawasaki triple, a Japanese motorcycle produced between 1969 and 1980 * Triumph Triple, a motorcycle engine from Triumph Motorcycles Ltd * A straight-three engine * A semi-truck with three trailers Science and technology * Triple (mathematics) (3-tupl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queue Number
In the mathematical field of graph theory, the queue number of a Graph (discrete mathematics), graph is a graph invariant defined analogously to book thickness, stack number (book thickness) using Queue (abstract data type), first-in first-out (queue) orderings in place of Stack (abstract data type), last-in first-out (stack) orderings. Definition A queue layout of a given graph is defined by a total ordering of the vertex (graph theory), vertices of the graph together with a partition of the edge (graph theory), edges into a number of "queues". The set of edges in each queue is required to avoid edges that are properly nested: if and are two edges in the same queue, then it should not be possible to have in the vertex ordering. The queue number of a graph is the minimum number of queues in a queue layout.. Equivalently, from a queue layout, one could process the edges in a single queue using a Queue (abstract data type), queue data structure, by considering the vertices in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
