On the connectivity of close to regular multipartite tournaments Original Research Article

If x is a vertex of a digraph D, then we denote by image and image the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by image over all vertices x and y of D (including image) and the local irregularity of a digraph D is image over all vertices x of D. Clearly, image. If image, then D is regular and if image, then D is almost regular.κ(D)⩾|V(D)|-|Vc|-2il(D)3κ(D)⩾|V(D)|-|Vc|-2il(D)+13κ(D)⩾|V(D)|-|Vc|+13