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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 .
Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər; [b] German: [ˈleːɔnhaʁt ˈʔɔʏlɐ] ⓘ, Swiss Standard German: [ˈleɔnhard ˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer.
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.
Harary invented this branch of graph theory, [8] [9] which grew out of a problem of theoretical social psychology investigated by the psychologist Dorwin Cartwright and Harary. [10] Applications of graph theory in numerous areas, especially to social science such as balance theory, opinion dynamics, and the theory of tournaments. [11]
The resulting mathematical structure is a graph. → → Since only the connection information is relevant, the shape of pictorial representations of a graph may be distorted in any way, without changing the graph itself. Only the number of edges (possibly zero) between each pair of nodes is significant.
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]
In graph theory, two of Petersen's most famous contributions are: the Petersen graph, exhibited in 1898, served as a counterexample to Tait's ‘theorem’ on the 4-colour problem: a bridgeless 3-regular graph is factorable into three 1-factors and the theorem: ‘a connected 3-regular graph with at most two leaves contains a 1-factor’.
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants.