Intro to Graph Theory | Definitions & Ex: 7 Bridges of Konigsberg
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- Опубліковано 2 жов 2024
- Leonhard Euler, a famous 18th century mathematician, founded graph theory by studying a problem called the 7 bridges of Konigsberg. Could one travel over a connection of landmasses and bridges hitting each bridge exactly once? This motivated abstract study and graph theory was born.
We formally define the concept of a graph, and talk about how to form graphs form real world examples. Finally we introduce the idea of a "Graph Isomorphism" which loosely says that if we keep the same vertices and edges (but maybe relabel them) then we can move their configuration around when drawing as much as we like as long as all the relationships are the same. The more precise technical definition is the following:
A Graph Isomorphism between two graphs (V1, E1) and (V2,E2) is a bijective function f from V1 to V2 such that any two vertices a and b in V1 have an edge in E1 connecting them if and only if f(a) and f(b) have an edge in E2 connecting them.
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I appreciated the connection to social media, we really are all just nodes.
Sir taking infinity respect for sharing your great knowledge...we are so much great full to you
excellent quality very underrated channel
You can walk through each bridge once, if you can swim!
When describing the graph with 1, 2, 3, 4, you missed an E...why didnt you connect (1, 3) ?? You seem to not have listed some connections at all.
Great video! I hadn't seen the relation between graphs and multisets until today. Is there a book with this approximation?
if you are interested professionally to the discrete math, i suggest you "discrete mathematics and its applications" from Kenneth H. Rosen
Amazing, technology merge with lessons.
Seems interesting! Keep em coming! Love your videos!
The bridge problem was also what started the donut=coffee mug madness called topology.
Sir please make video on Real Analysis
Sir You are one of the best teacher I have ever seen, please make videos on Real Analysis and Group Theory
just perfect! i don't even know how to describe these explanations, no comments! Well done! Thanks a lot! I have not seen these kinda explanations for the graph theory.
Thank you!!
Should I watch entire playlist as someone who is trying to become a self learned programmer
yes
@@yousefabdelgaber7498 100% yes. This is an amazing series.
I really thank u
I have an exam of this graph theories tomorrow and u helped me to figure out what is going on
Yayy 😊😊
Brilliant ❤️❤️
How do you represent a graph on a computer?
If you have n nodes, create a list with size n. Every item is another list, containing the index of what nodes it's connected to. If you want weights, every item of that list must be a pair (index, weight). That's a representation called adjacency list.