graphs and networks

Question 1

graph

Answer 1

set of points joined by lines

Question 2

arc

Answer 2

line segment (one point to another)/edge

Question 3

node

Answer 3

point/vertex

Question 4

trail

Answer 4

sequence of arcs - continuous arc to arc journey

Question 5

path

Answer 5

trail but with no repeated nodes

Question 6

cycle

Answer 6

trail that ends where it started that does not repeat any node

Question 7

tree

Answer 7

connected graph with no cycles

Question 8

connected graph

Answer 8

graph where there exists a path to join to any node to any other

Question 9

complete graph (Kn)

Answer 9

each node is directly connected to every other node at least once

Question 10

bipartite graph (K,n,m)

Answer 10

graph consisting of two sets of nodes with arcs joining between the 2 sets

Question 11

order of a node

Answer 11

number of arcs meeting at the node

Question 12

planar graph

Answer 12

graph that can be drawn so that arcs only meet at nodes

Question 13

simple graph

Answer 13

a graph with no loops or multiple arcs

Question 14

eulerian graph

Answer 14

graph where all nodes are even and connected & that can be drawn with one continuous node, ending where it started

Question 15

semi-eulerian graph

Answer 15

graph with 2 odd nodes and the rest are even - all are connected
& can be drawn with one continuous line starting at one odd node and ending at the other

Question 16

Euler’s relationship?

Answer 16

nodes + regions = arcs + 2

Question 17

closed trail

Answer 17

first and last nodes are the same

Question 18

directed graph / di-graph

Answer 18

a graph in which the edges/arcs have a direction

Question 19

incidence matrix

Answer 19

a matrix representing the edges in a graph

Question 20

hamiltonian cycle

Answer 20

a cycle that visits every node

Question 21

spanning tree properties

Answer 21

(n-1) arcs, n nodes, all connected, no cycles