A new graph parameter, edge neighbor toughness is introduced to measure how difficult it for a be broken into many components through the deletion of closed neighborhoods few edges. Let G=(V,E) graph. An e said subverted when its neighborhood and two endvertices are deleted from G. set S⊆E(G) called an cut-strategy if all edges in S has been G survival subgraph, denoted by G/S, disconnected, or...

The purpose of this paper is to study optimality of circular neighborbalanced block designs when neighbor effects are present in the model. In the literature many optimality results are established for direct effects and neighbor effects separately, but few for total effects, that is, the sum of direct effect of treatment and relevant neighbor effects. We show that circular neighbor-balanced de...

Rees (1967) introduced neighbor designs in serology. Since then it is well investigated field. Neighbor balanced designs are more useful to remove the neighbor effects in experiments where the performance of a treatment is affected by the treatments applied to its neighboring plots. Neighbor designs ensure that treatment comparisons will be less affected by neighbor effects as possible. This pa...