What is a Path Graph? | Graph Theory

What is a path graph? We have previously discussed paths as being ways of moving through graphs without repeating vertices or edges, but today we can also talk about paths as being graphs themselves, and that is the topic of today's math lesson!
A path graph is a graph whose vertices can be labeled v_1, v_2, ..., v_n such that the edge set of the graph is given by { { v_i, v_{i+1} } | 1 is less than or equal to i is less than or equal to n }. Take a look at the first few path graphs in the video lesson, and you will surely see what structure these graphs have. They also have the unique property that they can be drawn entirely in a straight line, very cool!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: vallow.bandcamp.com/
Vallow Spotify: open.spotify.com/artist/0fRtu...
Vallow SoundCloud: / benwatts-3
********************************************************************
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: / wrathofmathlessons
Follow Wrath of Math on...
● Instagram: / wrathofmathedu
● Facebook: / wrathofmath
● Twitter: / wrathofmathedu
My Music Channel: / seanemusic

[@PunmasterSTP]

Path graph? More like "Perfect presentations, that can help us to grasp!"

[@LearningCS-jp4cb]

Was about to skip this video thinking it was duplicate of "what is a path in graph?". Glad I didn't skip

[@asbjrnfeenstra2079]

Absolutely brilliant 👌

[@WrathofMath]

Thank you!

[@abdulwahab-3]

Excellent
Thank you very much

[@joejoelinks9335]

Thanks I leaned something

[@Sgh591]

Loved the lesson! Thanks !
Could you please explain Veblen 's theorem and provide its proof? If so, would be really thankful.

[@WrathofMath]

Glad to help! I'll look into it and see what I can do!

[@user-dg4xj5cs9h]

Good Day! A path can't revisit the visited vertices but is it allowed in Strongly connected?

[@annakbanana861]

So for P_4 path graph how would one go about to prove that it is connected?

[@WrathofMath]

By definition of P4, there exists a labeling of its vertices v1, v2, v3, v4, so that Q=(v1,v2,v3,v4) is a path. Then, given any two vertices vi and vj, we could travel between them by starting at one and then moving towards the other on the path Q. Thus the graph is connected.

[@luciano8158]

yo the fast forwarding for v1, v2, v3 at ~3:30 was really scary. true for anyone else?

[@WrathofMath]

Occasionally when editing I find a particular part takes way too long, often because I am explaining something simple but which takes a long time to say. Or when I am listing out things. On these occasions I sometimes speed up the video, and I often think of how it may startle the viewer or make them think their device is glitching, still not sure if it's ever actually a good idea because of that haha.

[@PunmasterSTP]

It took me by surprise too, but maybe it's good to have parts like that so they can keep us on our toes and paying attention.

[@novulus5470]

So a path graph is basically a graph where there exists a path where all the vertices lie on it right?

[@WrathofMath]

Yes you could say that!

[@mayur_madhwani03]

wow

[@WrathofMath]

Thanks for watching, I hope it helped! If you're looking for more graph theory, check out my playlist: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html