Assume that G does not equal K_2.
K_2 is the complete 2-partite graph
If G is regular of degree "r" and Kappa(G) = 1, prove that λ(G) <= [floor function of "r / 2" ]
The floor function, also called the greatest integer function or integer value, gives the largest integer less than or equal to "r / 2."
DEFN: the edge connectivity, λ(G), is the minimum number of edges whose removal makes G disconnected or trival.
Without loss of generality, we can assume that the graph is connected. Now, K_2 is the only 1-regular graph (graph of regularity 1). Hence we have G r-regular with r >= 2.
Consider any graph such that Kappa(G) = 1. By definition of Kappa, there ...
This is a proof regarding a floor function.