Discrete Graph Theory book or literature that dives into these concepts

[Terrell]

I need recommendations on literature to read. Basically i do not understand these section of Frank Harary's book on graph theory since the definition of what a boundary and a cycle vector is not clearly defined. I have googled literature on it but I am having a tough time finding the right literature. I attached an image of a page in the book. please see below. thanks!

 

[The Bill]

You might want to try the Wikipedia article for cycle spaces: https://en.m.wikipedia.org/wiki/Cycle_space

Note that the finite field \mathbb Z^2 is the same as what Harary calls \mathbb F_2.

Also, he's using the word boundary to mean endpoints. A closed loop has no endpoints. His choice of language makes sense because he's speaking topologically. Look up some literature on chains and boundaries in topology and you can see how subsets of graphs are very simple examples of chains in topology.

The Wikipedia article I linked has a decent list of references you might want to check some of, by the way.