graph theory

Definition

The branch of mathematics dealing with the properties of graphs (networks of vertices and edges).

Example Sentences

• "The type of graph studied in graph theory is formally described as an ordered pair G#61;(V,E) comprising a set V of vertices, or nodes, and a set E of pairs (either ordered or unordered) of vertices, each representing an (directed or undirected) edge; if desired, the vertices and/or edges can be labelled."
• "In graph theory there are two concepts of "sameness" whereby graphs are judged to be "the same", namely equality and isomorphism.[…]An indication of the pervasive role isomorphism has in graph theory is the fact that isomorphism has virtually captured the word "is"."
• "Extremal problems are at the very heart of graph theory. Interpreting it broadly, extremal graph theory encompasses most of graph theory, in its narrow sense, it contains many of the deepest and most beautiful results in graph theory."