Part a
Given a directed graph representing a city’s routing network, explain how to determine whether an Eulerian circuit exists by verifying the in-degrees and out-degrees for each vertex. Describe the method for identifying any vertex imbalance.
Matrix-Based Graph Analysis for Connectivity
Consider a directed graph representing a network of 5 cities. The connections between the cities are recorded in an adjacency matrix A where the entry \(a_{ij}\) is 1 if there is a direct route from city i to city j, and 0 otherwise. The adjacency matrix A is given as follows: \( A = \begin{bmatrix} […]