in Graphs : connectivity, matching, coloring is there in syllabus .
From Rosen - connectivity, euler and hamilton paths , coloring is in chapter 10 - 10.4, 10.5, 10.8
From narsingh deo Chapter no 2 - 2-5, 2-6, Chapter no 4 - 4-5 [ connectivity] ,
Chapter no 8 - 8-1, 8-2, 8-4, 8-6 , so 4 color theorem , Independent set is imp from graph coloring.
Imp points -- > Different types of graph and there properties : vertex and edge connectivity , separable graph , k-connected graph , connected component, matching , graph coloring ( 4 color theorem ) ,
Euler and Hamiltonian Graphs , konigsberg Bridge problem, Independent set of vertices , chromatic number are important .
Video :
https://www.youtube.com/user/DrSaradaHerke/playlists?view=50&sort=dd&shelf_id=5