In this study, generalized k-order Fibonacci hybrid quaternion is defined. We give recurrence relation, generating function, the summation formula and some properties for these quaternions. Furthermore, matrix representation quaternions determined. The Q_k defined numbers given By means of another matrices, several identities are also obtained.

The generalized k-connectivity κk(G) of a graph G was introduced by Chartrand et al. in 1984. It is natural to introduce the concept of generalized k-edge-connectivity, λk(G). For general k, the generalized k-edgeconnectivity of a complete graph is obtained. For k ≥ 3, tight upper and lower bounds of κk(G) and λk(G) are given for a connected graph G of order n, namely, 1 ≤ κk(G) ≤ n− k2 and 1 ≤...