2024 : 11 : 21
Doost Ali Mojdeh

Doost Ali Mojdeh

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
HIndex:
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Phone: 011-35302448

Research

Title
Neighbor Locating Coloring on Graphs: Three Products
Type
JournalPaper
Keywords
Coloring, Neighbor locating coloring, (Cartesian, lexicographic and corona) product, Graphs
Year
2024
Journal Journal of Combinatorial Mathematics and Combinatorial Computing
DOI
Researchers Ali Ghanbari ، Doost Ali Mojdeh

Abstract

Let G be a simple fnite graph. A k-coloring of G is a partition π = {S1, · · · , Sk} of V (G) so that each Si is an independent set and any vertex in Si takes color i. A k-coloring π = {S1, · · · , Sk} of V (G) is a neighbor locating coloring if any two vertices u, v ∈ Si, there is a color class Sj for which, one of them has a neighbor in Sj and the other not. The minimum k with this property, is said to be neighbor locating chromatic number of G, denoted by χNL(G) of G. We initiate to study the neighbor locating coloring of graphs resulted from three types of product of two graphs. We investigate the neighbor locating chromatic number of Cartesian, lexicographic and corona product of two graphs. Finally, we untangle the neighbor locating chromatic number of any aforementioned three products of cycles, paths and complete graphs.