Answer to Question #76665 in Discrete Mathematics for Keith

Question

Describe two situations that can be modelled with a Tree. Describe the graph model that you will use.

Answer 1

1) Let’s consider a country N in which there are some cities and some roads connecting cities. Let there is an unique way between each two cities in N.
This country can be represented in Tree as follows. Vertexes of the tree will correspond to cities and two vertexes will be connected by edge if and only if there is a road between the corresponding to these vertexes cities. Since there is only one way between each two vertex this graph is a tree, QED.
2) ) Let there is an airline X which has flights to all countries in the world. We know that using this airline we can from each country get to each other. Also we know that any X’s flights don’t form a cycle.
This country can be represented in Tree as follows. Vertexes of the tree will correspond to countries and two vertexes will be connected by edge if and only if there is a flight between the corresponding to these vertexes countries. Since a way exist between each two vertex in this graph and also there isn’t any cycles this graph is a tree, QED.