@article{Upper Distance k-Cost Effective Number in the Join of Graphs_2020, place={Maryland, USA}, volume={13}, url={https://ejpam.com/index.php/ejpam/article/view/3657}, DOI={10.29020/nybg.ejpam.v13i3.3657}, abstractNote={Let k be a positive integer and G be a connected graph. The open k-neighborhood set Nk G(v) of v âˆˆ V (G) is the set Nk G(v) = {u âˆˆ V (G) \ {v} : dG(u, v) â‰¤ k}. A set S of vertices of G is a distance k- cost effective if for every vertex u in S, |Nk G(u) âˆ© Sc| âˆ’ |NkG(u) âˆ© S| â‰¥ 0. The maximum cardinality of a distance k- cost effective set of G is called the upper distance k- cost effective number of G. In this paper, we characterized a distance k- cost effective set in the join of two graphs. As direct consequences, the bounds or the exact values of the upper distance k- cost effective numbers are determined.}, number={3}, journal={European Journal of Pure and Applied Mathematics}, year={2020}, month={Jul.}, pages={701–709} }