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In mathematics and computer science, graph theory is the study of graphs, ... Archived (PDF) from the original on 2019-05-17. Gibbons, Alan (1985).
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 with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
Given a graph, deciding whether it is the square of another graph is NP-complete. [16] Moreover, it is NP-complete to determine whether a graph is a k th power of another graph, for a given number k ≥ 2, or whether it is a k th power of a bipartite graph, for k > 2. [17]
In addition to over 350 research papers on mathematics, Bollobás has written several books, including the research monographs Extremal Graph Theory in 1978, Random Graphs in 1985 and Percolation (with Oliver Riordan) in 2006, the introductory books Modern Graph Theory for undergraduate courses in 1979, Combinatorics and Linear Analysis in 1990 ...
In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph , find the maximal number of edges (,) an -vertex graph can have such that it does not have a subgraph isomorphic to .
Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...