June 10, 2023
Doost Ali Mojdeh

Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences


Title Dominated Coloring of Certain Graphs
Type Article
Dominated coloring, Dominated chromatic covering, Dominated chromatic covering number
Journal global analysis and discrete mathematics
DOI 10.22128/gadm.2022.624.1081
Researchers Fatemeh Choopani (First researcher) , Abbas Jafarzadeh (Second researcher) , Doost Ali Mojdeh (Third researcher)


A proper coloring of a graph G is called a dominated coloring whenever each color class is dominated by at least one vertex. The minimum number of colors among all dominated colorings of G is called its dominated chromatic number, denoted by χdom(G). We define a parameter related to dominated coloring, namely dominated chromatic covering. For a minimum dominated coloring of G, a set of vertices S is called a dominated chromatic covering if each color class is dominated by a vertex of S. The minimum cardinality of a dominated chromatic covering of G is called its dominated chromatic covering number, denoted by θχdom(G). It is clear that θχdom(G) ≤ χdom(G). In this paper, we obtain the dominated chromatic number and θχdom(G) when G is middle and total graph of paths and cycles.