@article{Cai2025, 
author = {Gaixiang Cai and Fengru Xiao and Guidong Yu},
title = {The identification numbers of lollipop graphs},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {7813-7827},
keywords = {lollipop graph, identification number, d-vector, diameter, ID-coloring},
url = {https://www.sciopen.com/article/10.3934/math.2025358},
doi = {10.3934/math.2025358},
abstract = {A nontrivial connected graph    G with diameter    d can be assigned a red-white coloring, where the vertices of    G are colored either red or white, with the stipulation that at least one vertex must be red. Associated with each vertex    v of    G is a    d-vector, called the code of    v, whose    ith coordinate is the number of red vertices at distance    i from    v. A red-white coloring of    G for which distinct vertices have distinct codes is called an identification coloring or    I  D-coloring of    G. A graph    G possessing an    I  D-coloring is called an    I  D-graph. The minimum number of red vertices among all    I  D-colorings of an    I  D-graph    G is the identification number or    I  D-number of    G. The number of red vertices in an identification coloring is called the identification coloring number. This article studied the identification coloring number of lollipop graphs by constructing vertex colorings.}
}