The connectivity of the SEE-graph and AEE-graph for the connected spanning k-edge subgraphs of a graph

In this paper, we show that the connectivity of the SEE -graph for the connected spanning k -edge subgraphs of a graph G is equal to the minimum degree of the SEE -graph, and the connectivity of the AEE -graph for the connected spanning k -edge subgraphs of a graph G is at least m - k , where m = | E ( G )|. Examples are given for showing that the lower bound is in some sense best possible. These results give best lower bounds for the numbers of times that many interpolating invariant values are attained over the set of all connected spanning k -edge subgraphs of a graph G . If k = | V ( G )| − 1, we get the results for spanning trees of a graph G .