Discrrete mathematics for computer science digraphs and relations

Digraphs and Relations... reflexivity For any digraph G, G* is reflexive... G* is the reflexive transitive closure of the binary relation G Reflexive Transitive Closure... weak partial

Digraphs and Relations

R is a transitive if

R = G + for some digraph G

transitivity

reflexivity For any digraph G,

G* is reflexive

G* is the reflexive transitive closure

of the binary

relation G

Reflexive Transitive

Closure

two-way walks

If there is a walk from

u to v and a walk back

from v to u then u and v

are strongly connected

u G* v AND v G* u

relation R on set A

is symmetric if

a R b IMPLIES b R a

(weak) partial orders

R is a W PO if

R = D * for some DAG D

weak partial

orders

transitive, symmetric &

reflexive

equivalence

relations

Equivalence Relation

An equivalence relation decomposes the domain into subsets called equivalence

same equivalence class

In the digraph of an equivalence relation, all the members of an equivalence

class are reachable from each other but not from any other equivalence class

Graphical Properties of

Relations Reflexive

Transitive

Symmetric

Equivalence Relation

Finis