TY - JOUR
ID - 287
TI - Dominated Coloring of Certain Graphs
JO - Global Analysis and Discrete Mathematics
JA - GADM
LA - en
SN - 2476-5341
AU - Choopani, Fatemeh
AU - Jafarzadeh, Abbas
AU - Mojdeh, Doost Ali
AD - Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
AD - Department of
Mathematics, Quchan University of Technology, Quchan, Iran
AD - Department of Mathematics, University of Mazandaran, Babolsar, Iran
Y1 - 2022
PY - 2022
VL - 7
IS - 1
SP - 89
EP - 99
KW - Dominated coloring
KW - dominated chromatic covering
KW - dominated chromatic covering number
DO - 10.22128/gadm.2022.624.1081
N2 - 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.
UR - https://gadm.du.ac.ir/article_287.html
L1 - https://gadm.du.ac.ir/article_287_6ee28d4d597d24bb863fc400911de72a.pdf
ER -