On ON LOCATING-DOMINATING SET OF THE CARTESIAN PRODUCT OF COMPLETE BIPARTITE GRAPHS AND A PATH OF ORDER TWO

Saputro, Suhadi Wido
As-Shidiq, Ikhsan Rizqi Az-Zukruf

Jurnal Matematika UNAND
Vol. 14 No. 3 (2025)

A set D is called as a locating-dominating set of a graph G if D is a dominating set of G such that every vertex outside D is uniquely identified by its neighbourhood within D. The locating-dominating number of G is the minimum cardinality of all locating-dominating sets of G. In this paper, we consider a Cartesian product graphs between a complete bipartite graphs Km1,m2 and a path of order two P2, denoted by Km1,m2P2. In particular, we determine the locating-dominating number of Km1,m2P2 for any values m1 and m2 at least 2.