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

## Authors

• Rolando N. Paluga
• Imelda S. Aniversario

## 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 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.

2020-07-31

## Section

Nonlinear Analysis

## How to Cite

Upper Distance k-Cost Effective Number in the Join of Graphs. (2020). European Journal of Pure and Applied Mathematics, 13(3), 701-709. https://doi.org/10.29020/nybg.ejpam.v13i3.3657