Reference no: EM132434393

• A graph is complete if and only if all the elements of its adjacency matrix except those on the main diagonal are equal to 1, i.e., A[i, j] = 1 for every 1 ≤ i, j ≤ N, i !=j
• A graph has a loop if and only if its adjacency matrix has an element equal to 1 on its main diagonal, i.e., A[i, i]= 1 for some 1 ≤ i ≤ N.
• An (undirected, without loops) graph has an isolated vertex if and only if its adjacency matrix has an all-zero row.

Given the adjacency matrix A for a graph of N vertices, give an algorithm to check if:

A. the graph is complete (vertex labels are 0 .. N-1)

B. the graph has a self-loop

C. the graph has an isolated vertex