METRIC DIMENSION OF COMPLETE SPLIT GRAPHS

Abstract

In this paper, the problem of determining the metric dimension for special class of graphs, named complete split graphs 𝐾^∗_{𝑘,𝑛−𝑘} is considered. It is stated and proved formula for the metric dimension of this graphs: for 𝑛 − 𝑘 ≥ 2 and 𝑘 ≥ 2, as well as for 𝑘 = 1 and 𝑛 ≥ 3, metric dimension of 𝐾^∗_{𝑘,𝑛−𝑘} is equal to n −2, otherwise metric dimension of 𝐾^∗_{𝑘,𝑛−𝑘} is equal to 𝑛 − 1.