graphs and networks

Question 1

simple graph

Answer 1

has no loops or multiple edges

Question 2

isolated vertex

Answer 2

a vertex with a degree of 0

Question 3

degenerate graph

Answer 3

no edges

Question 4

connected graph

Answer 4

all vertices are connected, indirectly or directly

Question 5

complete graph

Answer 5

all vertices are connected directly to every other vertex

Question 6

bridge

Answer 6

an edge, where if removed, will cause the graph to become disconnected

Question 7

sub graph

Answer 7

a part of a larger graph

Question 8

equivalent graph (isomorphic)

Answer 8

a graph that looks different, but contains the same information

Question 9

planar graph

Answer 9

a graph that can be drawn with no intersections of edges

Question 10

faces

Answer 10

an area enclosed by edges, includes the outside of the graph

Question 11

Eulers rule

Answer 11

v-e+f=2

Question 12

walk

Answer 12

any continuous sequence of edges

Question 13

trail

Answer 13

a walk with no repeated edges

Question 14

path

Answer 14

a trail with no repeated vertices

Question 15

circuit

Answer 15

a trail that starts and finishes at the same vertex

Question 16

cycle

Answer 16

a circuit with no repeated vertices

Question 17

Eulerian trial

Answer 17

follows every edge of the graph
exists if graph has 2 vertices with an odd degree
does not repeat edges

Question 18

Eulerian circuit

Answer 18

an Eulerian trail that starts and finishes at the same vertex
exists if all vertices have an even degree
does not repeat edges

Question 19

Hamiltonian path

Answer 19

visits every vertex of a graph

does not repeat vertices

Question 20

Hamiltonian cycle

Answer 20

same as Hamiltonian path but starts and ends at the same vertex
does not repeat vertices

Question 21

weighted graph

Answer 21

numbers associated to edges