%0 Journal Article
%T Dominated Coloring of Certain Graphs
%J Global Analysis and Discrete Mathematics
%I Damghan University Press
%Z 2476-5341
%A Choopani, Fatemeh
%A Jafarzadeh, Abbas
%A Mojdeh, Doost Ali
%D 2022
%\ 11/01/2022
%V 7
%N 1
%P 89-99
%! Dominated Coloring of Certain Graphs
%K Dominated coloring
%K dominated chromatic covering
%K dominated chromatic covering number
%R 10.22128/gadm.2022.624.1081
%X 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.
%U https://gadm.du.ac.ir/article_287_6ee28d4d597d24bb863fc400911de72a.pdf