Graph

• graph is a pair of two sets where– set of elements called vertices (singl. vertex)– set of pairs of vertices (elements of ) called edges

• Example: where

• Notation: – we write for a graph with vertex set and edge set – is the vertex set of , and is the edge set of

1

2

3 4

drawing of

- traffic modelingMAXIMUM FLOW

- shortest (fastest) routeSHORTEST PATH

- efficient distribution, logistics, pickup/deliveryHAMILTONIAN PATH/CYCLE,TRAVELLING SALESMAN PROBLEMCHINESE POSTMAN PROBLEM

Network Modeling (rail, road, airline)Applications

- circuit layout, VLSIGRAPH DRAWING PLANARITY

- communication protocolsDIAMETER, RADIUSSPANNING TREEDOMINATING SET

- fault-tolerant networksMINIMUM CUTCONNECTIVITY

ApplicationsNetwork Modeling (electrical, communication)

Applications- Job scheduling / Critical path

GRAPH COLOURINGMAXIMUM CLIQUE

- Job AssignmentMAXIMUM MATCHINGSTABLE MARRIAGE PROBLEM

- Evolutionary trees (Biology)TREE DECOMPOSITION

Modeling conflict / compatibility / relationship