Let G be a graph and α(G) be the independence number of G. For a vertex v ∈ V (G), d(v) and N(v) represent the degree of v and the neighborhood of v in G, respectively. In this paper, we prove that if G is a k-connected graph of order n, and if max{d(v) : v ∈ S} ≥ n/2 for every independent set S of G with |S| = k which has two distinct vertices x, y ∈ S satisfying 1 ≤ |N(x) ∩N(y)| ≤ α(G)− 1, th...

The study of Hamiltonian graphs began with Dirac’s classic result in 1952. This was followed by that of Ore in 1960. In 1984 Fan generalized both these results with the following result: If G is a 2-connected graph of order n and max{d(u), d(v)}≥n/2 for each pair of vertices u and v with distance d(u, v)=2, then G is Hamiltonian. In 1991 Faudree–Gould–Jacobson–Lesnick proved that if G is a 2-co...

classical control methods such as pontryagin maximum principle and bang-bang principle and other methods are not usually useful for solving opti-mal control systems (ocs) specially optimal control of nonlinear systems (ocns). in this paper, we introduce a new approach for solving ocns by using some combination of atomic measures. we define a criterion for controllability of lumped nonlinear con...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...