Is there any undergraduate textbook on graph theory using linear algebra? A request is a beginning with graph matrices that explain most concepts in graph theory?
P.s. This thread has more specific requests than this thread What are good books to learn graph theory?.
On
I collect some books below
Graphs and Matrices by Bapat (as pointed out by Josse)
Section 1.9 of Graph Theory: Springer Graduate Text GTM 173 By Reinhard Diestel covers linear algebra on graphs (2012, P.24)
Section 4.6 of Graph Theory and Its Applications, Second Edition By Jonathan L. Gross, Jay Yellen (2005, p.197) covers, similarly.
Handbook of Graph Theory (2014), 2nd Edition by Gross et all (massive book) where Chapter 6.4 and the Chapter 6 on Algebraic Graph Theory (picture about the book here and Algebraic Graph Theory overview here)
where my favourite books bolded are the book by Bapat and the Handbook, nice reference material with over 1k pages. The Graphs and Vector Spaces subsection is written by Krishnaiyan "KT" Thulasiraman.
Related questions
First book on algebraic graph theory? (a bit broader perspective with things such as linear algebra, group theory, ...)
What are good books to learn graph theory? (more elementary focus)
There is one such book I know about: Ravindra B. Bapat – Graphs and Matrices. I don't have a lot of experience with this book, but I think this should be accessible at the undergraduate level. It also contains a lot of references for further reading, so it seems like a good starting point.
Apart from that, most books on algebraic graph theory contain some linear algebraic methods, but those may shift their focus more towards other algebraic methods such as graph automorphisms and various graph polynomials.