Write the adjacency matrix representation of the graph given in the figure. The graph has four vertices P1, P2, P3, P4 with edges P1-P2, P1-P3, P2-P4, and P3-P4 (a 4-cycle).

GATE 1988 · Discrete Mathematics · Graph Connectivity · medium

Answer: Adjacency matrix: Row P1=[0,1,1,0]; Row P2=[1,0,0,1]; Row P3=[1,0,0,1]; Row P4=[0,1,1,0].

1. Identify edges from the figure: Edges: P1-P2, P1-P3, P2-P4, P3-P4. Non-zero off-diagonal cells: (1,2),(2,1),(1,3),(3,1),(2,4),(4,2),(3,4),(4,3).
2. Fill the adjacency matrix: A = [[0,1,1,0],[1,0,0,1],[1,0,0,1],[0,1,1,0]]. Row P1=[0,1,1,0]; Row P2=[1,0,0,1]; Row P3=[1,0,0,1]; Row P4=[0,1,1,0].