Let P be a hereditary property. Let kP(G) denote the number of forbidden subgraphs, which are contained in G. A graph G is said to be weakly P-saturated, if G ∈ P and the edges of the complement of G can be labelled e1, e2, . . . , el in such way that for i= 0, 1, . . . , l− 1 the inequality kP(Gi+1)> kP(Gi) holds, whereG0=G,Gi+1=Gi + ei andGl =Kn. The minimum possible size of weakly P-saturate...

In this paper we introduce intuitionistic fuzzy completely regular weakly generalized continuous mappings and some of their properties are studied.

A graph G = (V, E) is called weakly four-connected if G is 4-edge-connected and G − x is 2-edge-connected for all x ∈ V . We give sufficient conditions for the existence of ‘splittable’ vertices of degree four in weakly four-connected graphs. By using these results we prove that every minimally weakly fourconnected graph on at least four vertices contains at least three ‘splittable’ vertices of...

in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

A labeled graph is said to be weakly bipartite if the clutter of its odd cycles is ideal. Seymour conjectured that a labeled graph is weakly bipartite if and only if it does not contain a minor called an oddK5. A proof of this conjecture is given in this paper. Let G = (V;E) be a graph and E. We call edges in odd and edges in E even. The pair (G; ) is called a labeled graph. A subset L E(G) is ...