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A graph with 6 vertices and 7 edges. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Euler devised a specific graph, the Speculum musicum, [118] [119] to illustrate the diatonico-chromatic genre, and discussed paths in this graph for specific intervals, recalling his interest in the Seven Bridges of Königsberg (see above). The device drew renewed interest as the Tonnetz in Neo-Riemannian theory (see also Lattice (music)). [120]
Its negative resolution by Leonhard Euler, in 1736, [1] laid the foundations of graph theory and prefigured the idea of topology. [ 2 ] The city of Königsberg in Prussia (now Kaliningrad , Russia ) was set on both sides of the Pregel River , and included two large islands— Kneiphof and Lomse —which were connected to each other, and to the ...
Graph Theory, 1736–1936 is a book in the history of mathematics on graph theory.It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the first textbook on the subject, published in 1936 by Dénes Kőnig.
A graph that contains a Hamiltonian path is called a traceable graph. A graph is Hamiltonian-connected if for every pair of vertices there is a Hamiltonian path between the two vertices. A Hamiltonian cycle , Hamiltonian circuit , vertex tour or graph cycle is a cycle that visits each vertex exactly once.
Here F is a functional graph, meaning a set of pairs where no two pairs have the same first member. On p. 77 (op. cit.) Bourbaki states (literal translation): "Often we shall use, in the remainder of this Treatise, the word function instead of functional graph." Suppes (1960) in Axiomatic Set Theory, formally defines a relation (p.
Euler invented the calculus of variations including its most well-known result, the Euler–Lagrange equation. Euler also pioneered the use of analytic methods to solve number theory problems. In doing so, he united two disparate branches of mathematics and introduced a new field of study, analytic number theory.
William Playfair (22 September 1759 – 11 February 1823) was a Scottish engineer and political economist. [1] The founder of graphical methods of statistics, [2] Playfair invented several types of diagrams: in 1786 he introduced the line, area and bar chart of economic data, and in 1801 he published what were likely the first pie chart and circle graph, used to show part-whole relations. [3]