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 ed...

Graph connectivity theory is important in network implementations, transportation, routing and tolerance, among other things. Separation edges vertices refer to single points of failure a network, so they are often sought-after. Chandramouleeswaran et al. introduced the principle semiring valued graphs, also known as S-valued symmetry 2015. Since then, works on graphs such vertex dominating set...