Consider graphs G 2 and G 3 shown in Figure 8.1. From the adjacency and Laplacian spectra of the graphs, what can be commented on the connectivity of the graphs?
For graph G2, the zero eigenvalue of the Laplacian matrix has a multiplicity of 1. Therefore,
graph G1 is connected. However, For graph G2, the zero eigenvalue of the Laplacian matrix
has a multiplicity of 2. Therefore, graph G2 is not connected and has two separate connected
components.
Computer Science & Information Technology
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