%0 Journal Article
%T On the $sd_{b}$-critical graphs
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Zamime, Mohamed
%D 2024
%\ 12/01/2024
%V 13
%N 4
%P 363-375
%! On the $sd_{b}$-critical graphs
%K $b$-coloring
%K $b$-chromatic number
%K $sd_{b}$-critical graphs
%R 10.22108/toc.2023.137558.2069
%X 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})