Intro to Graph Theory | Definitions & Ex: 7 Bridges of Konigsberg

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.
►FULL DISCRETE MATH PLAYLIST: • Discrete Math (Full Co...
OTHER COURSE PLAYLISTS:
►CALCULUS I: • Calculus I (Limits, De...
► CALCULUS II: • Calculus II (Integrati...
►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivar...
►VECTOR CALCULUS (Calc IV): • Calculus IV: Vector Ca...
►DIFFERENTIAL EQUATIONS: • How to solve ODEs with...
►LINEAR ALGEBRA: • Linear Algebra (Full C...
OTHER PLAYLISTS:
► Learning Math Series
• 5 Tips To Make Math Pr...
►Cool Math Series:
• Cool Math Series
BECOME A MEMBER:
►Join: / @drtrefor
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): / treforbazett
►Instagram (photography based): / treforphotography

[@marissadevelops]

I appreciated the connection to social media, we really are all just nodes.

[@tanjinaaktar1146]

Sir taking infinity respect for sharing your great knowledge...we are so much great full to you

[@sauravuppoor2409]

Seems interesting! Keep em coming! Love your videos!

[@cocoarecords]

excellent quality very underrated channel

[@niiazbekmamasaliev9828]

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.

[@DrTrefor]

Thank you!!

[@aknerkan3428]

Amazing, technology merge with lessons.

[@nazanin2093]

I really thank u I have an exam of this graph theories tomorrow and u helped me to figure out what is going on

[@khaledaivr9906]

Brilliant ❤️❤️

[@dg4262]

You can walk through each bridge once, if you can swim!

[@maurocruz1824]

Great video! I hadn't seen the relation between graphs and multisets until today. Is there a book with this approximation?

[@emircantepe7382]

if you are interested professionally to the discrete math, i suggest you "discrete mathematics and its applications" from Kenneth H. Rosen

[@condogmcfluffin868]

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.

[@competitivedoritos4294]

Yayy 😊😊

[@SuperDeadparrot]

How do you represent a graph on a computer?

[@hemantsethia2475]

Sir please make video on Real Analysis

[@hemantsethia2475]

Sir You are one of the best teacher I have ever seen, please make videos on Real Analysis and Group Theory

[@anb4351]

Should I watch entire playlist as someone who is trying to become a self learned programmer

[@yousefabdelgaber7498]

yes

[@BlackCodeMath]

@@yousefabdelgaber7498 100% yes. This is an amazing series.