: Paths and Circuits (Ch. 2), Trees and Fundamental Circuits (Ch. 3), and Cut-Sets/Cut-Vertices (Ch. 4).
Many solutions in the later chapters require using Adjacency and Incidence matrices. Practice matrix multiplication to find the number of paths between vertices. 2. Focus on Planarity Graph Theory By Narsingh Deo Exercise Solution
Perhaps the greatest value in solving Deo's exercises is the exposure to classical algorithms in their native environment. Problems revolving around the shortest path (Dijkstra’s or Warshall’s algorithms), flow problems, and traveling salesman approximations are heavily featured. : Paths and Circuits (Ch
: Using graph theory to solve Kirchhoff’s laws and circuit equations. : Paths and Circuits (Ch. 2)
Proof: Let $G = (V, E)$ be a graph with $n$ vertices and $e$ edges. Every edge in a graph connects two vertices (or a vertex to itself in a loop). Therefore, every edge contributes 2 to the total sum of degrees.