TY - JOUR
TI - Upper Distance k-Cost Effective Number in the Join of Graphs
PY - 2020/07/31
Y2 - 2024/06/19
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 13
IS - 3
LA - en
DO - 10.29020/nybg.ejpam.v13i3.3657
UR - https://doi.org/10.29020/nybg.ejpam.v13i3.3657
SP - 701-709
AB - 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.
ER -