@article {
author = {Zamime, Mohamed},
title = {On the $sd_{b}$-critical graphs},
journal = {Transactions on Combinatorics},
volume = {13},
number = {4},
pages = {363-375},
year = {2024},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2023.137558.2069},
abstract = {A $b$-coloring of a graph\ $G$ is a proper coloring of its vertices such that each color class contains a vertex that has a neighbor in every other color classes. The $b$-chromatic number of a graph $G$, denoted by $b(G)$, is the largest integer $k$ such that $G$ admits a $b$-coloring with $k$ colors. Let $G_{e}$ be the graph obtained from $G$ by subdividing the edge $e $. A graph $G$ is $sd_{b}$-critical if $b(G_{e})