Game edge-connectivity of graphs

Recently, the authors introduced a game invariant of graphs, called connectivity. In this paper, we investigate edge version invariant, edge-connectivity, by introducing new combinatorial on graph, graph edge-cutting game. The is one generalizations classical game, named Shannon switching As an analog study have complete characterization graphs with edge-connectivity infinity in terms number edge-disjoint spanning trees. corollary above, any at least 4 has infinity. Thus, since determining given cubic most interesting problem, give useful tool to estimate graphs. Other than those many fundamental topics and propose several open problems.