graphs Flashcards
graphs application in general
1-0 computer networks
2- electrical circut
3-road maps
graphs uses in computer sciences
1-Social network (Facebook, LinkedIn)
2-Computer networks
3-Transportation network
4-Wireless sensors
Graph Categorization
1-➢ A Directed Graph or Digraph is a graph where each edge has a direction
The edges in a digraph are called Arcs or Directed Edges
.
2-➢ An Undirected Graph is a graph where the edges have no directions
The edges in an undirected graph are called Undirected Edges
3-A Weighted Graph is a graph where all the edges are assigned weights.
4-multi graph If the same pair of vertices have more than one edge, that graph is called
when do we call a graph multi-graph
If the same pair of vertices have more than one edge, that graph is called multi-graph
a dircted graph :
(1, 4) = 1→4 where ….. is the tail and …… is the head vertics
1 and 4
name of edges in dircted and undircted graphs
The edges in a digraph are called Arcs or Directed Edges
the edges in undircted graph are called Undirected Edges
what is digraph
dircted graph
graph terminoalgy define all below
1- adjacent vertices
2-incidents
3-loop or(……complete)
4-simple graph
1- they are called adjecnt when theere is edge that connects thm like (1,4)
2-where there is edge like (1,4)its called an incident
3-loop or self edge when there is an edge thats connected to itself like (4,4) in the last graph
4- A graph that is undirected and does not have any loops or multiple edges
graph terminoalgy(part2) define all below
1-path
2-reachable vertices
3-simple bath
1-path : sequnce of edges in the graph
2-its reachable if there was a path between the two vertices
3-simple path is path where each node is visted once
graph terminoalgy part 3
define whats below
1-length
2-circut
3-cycle
length : sum of the lengtrh of the edges on the path
Circuit: A path whose first and last vertices are the same.
➢➢ The path 3,2,1,4,5,3 is a circuit
➢ Cycle: A circuit where all the vertices are distinct except for the first (and the last) vertex.
➢➢ 1,4,5,3,1 is a cycle, but 1,4,5,4,1 is not a cycle.
➢ Hamiltonian Cycle: A Cycle that contains all the vertices of the graph.
➢➢ 1,4,5,3,2,1 is a Hamiltonian Cycle.
T or F: there can be morew than one path between two vertices
T
graph terminoalgy part 4
define whats below
1-degree of the vertics
2-in-degree
3-out-degree
4-subgraph
5connected graph
1- degree in undircted graph is the number of edges or incicdents
2-in-degree in DIgraph the number of edges entering the vertex
3-out degree the number of edges leaving the vertex
4-sub graph ➢ A Subgraph of graph G=(V,E) is a graph H=(U,F) such that U Є V and F Є E
5-A graph is said to be Connected if there is at least one path from every vertex to every other vertex in the graph
what is the subgraph of this graph
graph terminoalgy (Last part)
1- connected graph
2- tree
3-forest
1-connected graph : if there was at least one path between every vertex in the graph
2-tree :Connected Undircted graph that contains no cycle
3-forest: graph that dose not contain a cycle
is this a forest or tree and why
its forest since tree needs to be connected