Upper Distance k-Cost Effective Number in the Join of Graphs

Authors

  • Julius Guhiting Caadan
  • Rolando N. Paluga
  • Imelda S. Aniversario

DOI:

https://doi.org/10.29020/nybg.ejpam.v13i3.3657

Keywords:

Distance k-cost effective set, upper distance k-cost effective number, join, t-fringe set, t- increment

Abstract

Let k be a positive integer and G be a connected graph. The open k-neighborhood set Nk G(v) of v ∈ V (G) is the set Nk G(v) = {u ∈ V (G) \ {v} : dG(u, v) ≤ k}. A set S of vertices of G is a distance k- cost effective if for every vertex u in S, |Nk G(u) ∩ Sc| − |NkG(u) ∩ S| ≥ 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.

Downloads

How to Cite

Caadan, J. G., Paluga, R. N., & Aniversario, I. S. (2020). Upper Distance k-Cost Effective Number in the Join of Graphs. European Journal of Pure and Applied Mathematics, 13(3), 701–709. https://doi.org/10.29020/nybg.ejpam.v13i3.3657