This page does not represent the most current semester of this course; it is present merely as an archive.
You have enough to worry about memorizing without keeping all these terms in your head. We intend to provide this list for your reference during every inclass evaluation relating to graphs.
Term  Definition 

Walk  An alternating sequence of vertices and edges

Path  A walk that does not visit any vertex twice 
Closed Walk  A walk that begins and ends at the same vertex 
Cycle  A closed walk that is a path except for its last vertex 
The related definitions on relations R : A \rightarrow A are
Term  Definition 

R is Reflexive  \forall x \in A \;.\; x R x 
R is Irreflexive  \forall x \in A \;.\; \lnot(x R x) 
R is Symmetric  \forall x,y \in A \;.\; (x R y) \rightarrow (y R x) 
R is Asymmetric  \forall x,y \in A \;.\; (x R y) \rightarrow \lnot(y R x) 
R is Antisymmetric  \forall x \neq y \in A \;.\; (x R y) \rightarrow \lnot(y R x) 
R is Transitive  \forall x,y,z \in A \;.\; (x R y) \land (y R z) \rightarrow (x R z) 
And those lead to these terms:
Term  Definition 

Strict partial order  transitive and asymmetric 
Weak partial order  transitive, reflexive, and antisymmetric 
Equivalence relation  transitive, reflexive, and symmetric 