Describe a discrete structure based on a graph that can be used to model airline routes and thei

Describe a discrete structure based on a graph that can be...

Key Concepts

Graph Theory

Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. In this context, airports are represented as vertices (nodes) and the airline routes connecting them as edges, making it a fundamental tool for modeling transportation networks and many other discrete systems.

Directed Graph

A directed graph, or digraph, is a type of graph in which the edges have orientations, indicating a one-way relationship between vertices. For airline routes, this helps to model the fact that a flight from one airport to another may not imply a return flight on the same path, capturing the directional nature of flight paths.

Weighted Graph

In a weighted graph, each edge is assigned a weight, which typically represents cost, distance, or time associated with traversing the edge. This is essential for modeling flight times on airline routes, as the weight on each edge can represent the duration or cost of a flight between two airports, allowing for computations such as the shortest travel time or least expensive route.

Transcript

00:01 We are asked to describe what the graph module for allies ' routes and flight time be like.

00:08 So if you choose to draw a graph that shows routes that airplane takes and their flight time, obviously the vertex is going to be airport, right? various airports that in the area that we want to cover and edges will be directed ages from one airport to another so it's obviously directed we also allow we will allow multiple ages for the reason that i will explain later and we have no loops obviously i believe there will be no like in case of emergency they will circle back around but that's not a plan that fly right so that we will not count that a flight usually will be from one place to another and the reason we want multiple edges here because normally a flight allies flight from one place to another will have multiple flight each day or weeks at at varying time so we should allow for multiple flight but how do we differentiate them that is the where the weight comes in so i said weight here is a term that describe when we have a graph and on each edges we assign some value or symbol that we want it doesn't have to be numbers i use the term with loosely so in this case case it will be the designated flight time for each separate flight right it will be something like it will be dead and time pretty much and if you want to describe this formally it would be a function from from the pair of vertices which represent edges right to here will be set of and whatever detail we want so date and time or something like that so each edges will be aside these value to describe the properties of whatever ages represent which in our case is flight time and that is why we want multiple edges because if we have just one edges we can put multiple time spot on them to represent different flights.

03:20 Now, that is it? so that is how, one way to do it...

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