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Doost Ali Mojdeh

Doost Ali Mojdeh

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

Research

Title
Dominated Coloring of Certain Graphs
Type
JournalPaper
Keywords
Dominated coloring, Dominated chromatic covering, Dominated chromatic covering number
Year
2022
Journal global analysis and discrete mathematics
DOI
Researchers Doost Ali Mojdeh ، Abbas Jafarzadeh ، Fatemeh Choopani

Abstract

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.