I am currently undergraduate student and I want to explore about coloring and domination of graphs. There are lot of materials on web related to this but asking advice like which resource or book to follow might help me in progressing.
I know the concept of coloring and I do not have any idea regarding domination in graphs. I will be thankful if someone provides links of resources or books which will be easy for me to follow as a beginner in the field.
The problem with studying any specific "sub-subdiscipline" in math, is that each one relates to many other topics within the broader topic. Coloring for example, relates closely to combinatorics or computational algorithms.
That being said, I used A First Course in Graph Theory by Chartrand and Zhang (2012) in my undergraduate days to learn about domination numbers and coloring. These have two good sections on these topics. Beyond that, finding easy-to-read texts specific to coloring and domination numbers gets tricky. Graph Theory by Diestel gives an up-to-date graduate level overview of graph theory in general, with a small section on coloring, and casual mentions of the topic in other chapters. However, discussion of domination is missing, probably because it is a settled NP-complete problem, so Chartrand might be the end of the story, beyond individual papers.