Networks and Matrices

Question 1

nodes or vertices

Answer 1

the points on a network

Question 2

edge

Answer 2

a line joining to nodes or vertices

Question 3

faces or regions

Answer 3

edges divide a graph up into seperate faces or regions

Question 4

loop

Answer 4

an edge that starts and ends at the same vertex or edge

Question 5

multiple edges

Answer 5

2 or more edges that connect to the same vertices

Question 6

weighted graph/weighted network

Answer 6

graphs that have amounts or distances or some information on each edge

Question 7

directed edges or arcs

Answer 7

an edge with significant direction shown with an arrow

Question 8

directed graph/network or digraph

Answer 8

any graph involving directed edges (or more)

Question 9

undirected graph/network

Answer 9

any graph with no directed edges

Question 10

simple graph/network

Answer 10

a graph or network with no loops, multiple edges or direction

Question 11

open walk

Answer 11

a walk which does not start and end at the same vertex

Question 12

closed walk

Answer 12

any walk that starts and ends at the same vertex

Question 13

open path

Answer 13

a walk that has no repeats of edges or vertices and does not start and end at the same vertex

Question 14

close path or cycle

Answer 14

a walk that has no repeats of edges or vertices and starts and ends at the same vertex

Question 15

path length

Answer 15

the number of edges a walk, path or cycle uses

Question 16

trail

Answer 16

a walk with no repeated edges (may have repeated vertices)

Question 17

connected graph

Answer 17

an undirected graph where every vertex is connected to one another

Question 18

disconnected or unconnected graph

Answer 18

a graph where a node or vertex is not joined by an edge

Question 19

complete graphs

Answer 19

simple graphs in which every vertex is connected to every other

Question 20

bridge

Answer 20

any edge which when removed makes a network become disconnected

Question 21

planar graph

Answer 21

a graph that can be drawn in the plane. doesn’t need to be connected. main feature is that it can always be drawn so that no two edges cross

Question 22

subgraph

Answer 22

when the vertices and edges of graph A are also vertices and edges of graph B, A is said to be subgraph of B

Question 23

Bipartite graph

Answer 23

a graph whose set of vertices can be split into two distinct groups in such a way that each edge of the graph joins a vertex in the first group to vertex in the second group

Question 24

Eularian graph

Answer 24

a connected graph is eulerian if it has a closed trail that includes every edge once only

Question 25

eularian trail

Answer 25

a connected graph that travels every edge once and only once, repeated vertices permitted, is a eulerian trail

Question 26

traversibility

Answer 26

to be able to complete all edges without repeat

Question 27

semi eulerian

Answer 27

a connected graph that’s an open trail that includes every edge only once is called semi eularian. they have two odd vertices and start and end at different odd vertices

Question 28

Hamiltonian path

Answer 28

a path in a graph that visits every vertex in a graph only once, with the possible exception of visiting the first vertex again at the end, thus making the path a cycle

Question 29

Hamiltonian cycle

Answer 29

a Hamiltonian cycle is a closed path that includes each vertex in a graph (except the first) only once

Question 30

semi hamiltonian

Answer 30

an open path that includes every vertex in a graph once