k-intersection graph of a finite set

For any nonempty set ω and k-subset λ, the kintersection graph, denoted by γm(ω,λ), is an undirected simple graph whose vertices are all msubsets of ω and two distinct vertices a and b are adjacent if and only if a∩b ⊈ λ. in this paper, we determine diameter, girth, some numerical invariants and planarity, hamiltonian and perfect matching of these graphs. moreover adjacency matrix is considered at the end.