The study of such graphs is called graph theory. Engineers need to find planarity in a graph when, for example, they are designing a computer chip without a crossed wire.

Refining with colors Mathematicians have developed various strategies to compare graphs. Since the 1970s, algorithms have been able to test graph isomorphism, but in exponential time.

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...

More by Gary Stix This article was originally published with the title “Graph Theory and Teatime” in Scientific American Magazine Vol. 296 No. 3 (March 2007) ...

Introduce students to nodes and graph theory and their use in operations research. Show how Dijkstra’s Algorithm can be used to find the shortest or quickest route between nodes in a network.

Long monochromatic paths in random graphs presented by Andrzej Dudek, Ph.D., Department of Mathematics, Western Michigan University Abstract: Recall that the size-Ramsey number of F, r^ (F, r), is the ...

The field of graph theory has been around since 1736, when Leonhard Euler published an article on the subject of the Seven Bridges of Königsberg (in Prussia, today’s Kaliningrad in Russia).

Each 9-by-9 sudoku grid is composed of nine 3-by-3 subgrids. Initially, some of these 81 squares contain a number, from 1 through 9, but others do not. The object is to fill in the empty squares ...

D. B. West, Introduction to Graph Theory, Prentice Hall 2001 R. Diestel, Graph Theory, Springer 2010. N. L. Biggs, Discrete Mathematics, OUP 2004 J.A.Bondy and U.S.R. Murty, Graph Theory with ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks—vertices (dots) and edges (lines connecting them)—has been an invaluable ...