Question

Let G be a connected nontrivial graph. Show that G ^ 2 is a block.

Answer 1

Horng solution on array let G be a non trivial connected graph Claimo G2 is block le. we have to show that graph and has no cent vecten G² is connected Now by the definition vertex set of G² to f edge set of G is of G o od same as vortex sub set of edge set of a set of ²] : G2 is connected ciG is connected) Now we have to show that G² has no cut verten We move this by contradiction & Assume that there is a cultverter of graph G² I let & be the cent vertex of graph G² Now, without loss of generality CULOG). Let 4 4 C₂ V are two componente of Gove Now vis wat vertex n a vertex in c. of venten in Cr such that there is edge i between that vortex inc, 4 vertex v auro vortex in C and verterin og The J v GG 4 verres ₂ G C har such that there is edge betweren v, 4r and edge between ₂ & v. Note that this edges cuv) and CV2iV) are in graph G. Because if they are not in G then G must be disconnected neelae set of G C edges of G2)