Give a formula for the degree of a vertex of L(G) (using the degrees in G). In which cases is L( ) an SRG? Let G be a connected graph. Find a necessary and sufficient condition for L(G) to be...

Give a formula for the degree of a vertex of L(G) (using the degrees in G). In which cases is L() an SRG? Let G be a connected graph. Find a necessary and sufficient condition for L(G) to be Eulerian. Conclude that the line graph of an Eulerian graph is likewise Eulerian, and show that the converse is false in general.