@article{Mari2024, 
author = {Baskar Mari and Ravi Sankar Jeyaraj},
title = {Radio number of    2  − super subdivision for path related graphs},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {8214-8229},
keywords = {channel assignment, radio labeling, radio number, path, complete bipartite, m−super subdivision},
url = {https://www.sciopen.com/article/10.3934/math.2024399},
doi = {10.3934/math.2024399},
abstract = {We studied radio labelings of graphs in response to the Channel Assignment Problem (CAP). In a graph    G  , the radio labeling is a mapping    ϖ  :  V  (  G  )  →  {  0  ,  1  ,  2  ,  .  .  .  ,  }  , such as        |    ϖ  (      μ    ′    )  −  ϖ  (      μ    ″    )      |    ≥  d  i  a  m  (  G  )  +  1  −  d  (      μ    ′    ,      μ    ″    )  . The label of    μ for under    ϖ is defined by the integer    ϖ  (  μ  )  , and the span under is defined by    s  p  a  n  (  ϖ  )  =  m  a  x  {      |    ϖ  (      μ    ′    )  −  ϖ  (      μ    ″    )      |    :      μ    ′    ,      μ    ″    ∈  V  (  G  )  }  .    r  n  (  G  )  =  m  i      n          ϖ        s  p  a  n  (  ϖ  ) is defined as the radio number of    G when the minimum over all radio labeling    ϖ of    G is taken.    G is said to be optimal if its radio labeling is    s  p  a  n  (  ϖ  )  =  r  n  (  G  )  . A graph H is said to be an    m super subdivision if    G is replaced by the complete bipartite graph        K          m      ,      m       with    m  =  2 in such a way that the end vertices of the edge are merged with any two vertices of the same partite set    X or    Y of        K          m      ,      m       after removal of the edge of    G. Up to this point, many lower and upper bounds of    r  n  (  G  ) have been found for several kinds of graph families. This work presents a comprehensive analysis of the radio number    r  n  (  G  ) for a graph    G, with particular emphasis on the    m super subdivision of a path        P          n       with    n  (  n  ≥  3  ) vertices, along with a complete bipartite graph        K          m      ,      m       consisting of    m v/ertices, where    m  =  2.}
}