Closed path = 1st Vertex = Last Vertex Simple path = different edges (Vertex can be used twice) Closed simple path: different edges + 1st vertex = last vertex (vertices can be used twice) Cycle = closed simple path (1st vertex = last vertex + different edges) + different vertices Distinct vertices ==> different edges Cycle= closed path e1…en of length at least 3 + distant vertices = path e1…en with n >= 3 + 1st vertex = last vertex + distinct vertices A path has all vertices distinct ==> different edges + no cycles G and H are isomorphic if there exists an isomorphism and γ = V(G) ---> V(H) such that if {u,v} edge in G then {γ(u), γ (v)} edge in H

each vertex goes to another vertex degrees are the same shapes are mapped too

to prove two graphs are isomorphic check the degree lists….if they match find a mapping between the two graphs

Euler path = simple path which goes through each edge exactly once Euler circuit = closed Euler path Theorem: A graph that has an Euler circuit must have all vertices of even degree

Graph: If 2 vertices of odd degree or ==> Euler path 0 vertices of odd degree