Graph Theory Vocabulary

If a complete graph has N vertices, how many edges does it have?

N(N-1)/2

Kn is

A complete graph with n vertices

A wheel Wn is

a cycle Cn with an additional vertex in the middle that is connected to each of the other vertices once.27

A bipartite graph is

a simple graph whose vertices can be partitioned into two disjoint sets V1 and V2 such that every edge in the graph connects a vertex in V1 to a vertex in V2 .

Complete graph contains

exactly one edge between each set of vertices

isomorphic graphs

have the same shape

Cycle consists of

n vertices v1, v2 , ..., vn and edges {v1 , v2}, {v2, v3}, ...,{vn-1 , vn }, and {vn , v1 }

multigraphs allow

parallel edges

psuedographs allow

parallel edges and loops

graph invariant

property preserved by isomorphism

A complete bipartite graph Km,n is a graph...

whose vertex set is partitioned into two subsets of m and n vertices and that has an edge between two vertices if and only if one vertex is in the first subset and the other vertex is in the other subset.