TY - JOUR
ID - 27887
TI - On the $sd_{b}$-critical graphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Zamime, Mohamed
AD - Department of Technology, University Yahia Fares of Medea, c.p 26000, Medea, Algeria
Y1 - 2024
PY - 2024
VL - 13
IS - 4
SP - 363
EP - 375
KW - $b$-coloring
KW - $b$-chromatic number
KW - $sd_{b}$-critical graphs
DO - 10.22108/toc.2023.137558.2069
N2 - 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})