A Linear Algorithm for Bipartite Drawing with Minimum Edge Crossings of Complete Binary Trees

Indonesian people have a high interest for public transportation. There are few kind of public transportation, and taxi is one of them. Taxi use taximeter to calculate passanger fares. Taximeters between taxi companies are different in term of results although using the same equation and principle. The total fare from the taximeter is based on equation that includes distance variable, speed of the vehicle, and time variable. People have a problem to choose taxi because of the differnces of taximeter fares and taxi pool. Based on the problem, the solution is an application to help customer to decide choosing taxi. The application will help customer by giving informations about taximeter and carpool form two different company. The informations are based on the distance of the start point and the finish point of the customer and based on the distances of the customer and the carpool of the taxy company that will processed trough the application to calculating the total fares for the customer between two taxi companies. By using algorithm for linear searching, customer will get the informations to help them to decide which taxi the customer will use. Keywords: Linear Algorithm, Taximeter, Google Apps, Choice, Taxi

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Join Products K2,3 + Cn

Mathematics ◽

10.3390/math8060925 ◽

2020 ◽

Vol 8 (6) ◽

pp. 925

Author(s):

Michal Staš

Keyword(s):

Bipartite Graph ◽

Complete Bipartite Graph ◽

Crossing Number ◽

Arithmetic Means ◽

Minimum Number ◽

Edge Crossings

The crossing number cr ( G ) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main goal of the paper is to state the crossing number of the join product K 2 , 3 + C n for the complete bipartite graph K 2 , 3 , where C n is the cycle on n vertices. In the proofs, the idea of a minimum number of crossings between two distinct configurations in the various forms of arithmetic means will be extended. Finally, adding one more edge to the graph K 2 , 3 , we also offer the crossing number of the join product of one other graph with the cycle C n .

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Improvement on the Crossing Number of Crossing-Critical Graphs

Discrete & Computational Geometry ◽

10.1007/s00454-020-00264-2 ◽

2020 ◽

Author(s):

János Barát ◽

Géza Tóth

Keyword(s):

Crossing Number ◽

Critical Graphs ◽

Minimum Number ◽

Edge Crossings

AbstractThe crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. A graph G is k-crossing-critical if its crossing number is at least k, but if we remove any edge of G, its crossing number drops below k. There are examples of k-crossing-critical graphs that do not have drawings with exactly k crossings. Richter and Thomassen proved in 1993 that if G is k-crossing-critical, then its crossing number is at most $$2.5\, k+16$$ 2.5 k + 16 . We improve this bound to $$2k+8\sqrt{k}+47$$ 2 k + 8 k + 47 .

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