@article{Gao2026, 
author = {Zhen-Bin Gao and Juan Chen and Feng-Xia Chen and Feng Liang},
title = {The edge balance properties of cubic graphs},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {5192-5218},
keywords = {cubic graph, edge-balance index set, generalized Petersen graph, 2n-cycle with warp and weft chords, X-strips graph, Issacs graph, Möbius ladder graph},
url = {https://www.sciopen.com/article/10.3934/math.2026212},
doi = {10.3934/math.2026212},
abstract = {For a simple, undirected graph    G  (  V  ,  E  ), let    f be an edge labeling    f:    E  →  {  0  ,  1  } such that, for any vertex    v and    i  ∈  {  0  ,  1  }, in the edges incident on    v, if the number of the edges labeled    i is more than the number of edges labeled    1  −  i, then the label of    v is defined by    i;    v is not defined otherwise. In a labeling graph of    G, let    i  ∈  {  0  ,  1  },        e    f    (  i  )  =      |    {  e  ∈  E  :  f  (  e  )  =  i  }      |   and        v    f    (  i  )  =      |    {  v  ∈  V  : the label of    v is    i  }      |  . After    f runs over all edge labelings satisfying        |        e          f        (  1  )  −      e          f        (  0  )      |    ≤  1, the set    {      |        v    f    (  1  )  −      v    f    (  0  )      |    :      |        e    f    (  1  )  −      e    f    (  0  )      |    ≤  1  } is called the edge-balance index set of graph    G, denoted by    E  B  I  (  G  ). In this paper, the set    {      v    f    (  1  )  −      v    f    (  0  )  :      |        e    f    (  1  )  −      e    f    (  0  )      |    ≤  1  } is called the full edge-balance index set of graph    G, denoted by    F  E  B  I  (  G  ). Some results are obtained on    F  E  B  I  (  G  ), and the relationship between    F  E  B  I  (  G  ) and    E  B  I  (  G  ) is discussed. By finding some closed trails, the    F  E  B  I and    E  B  I of some classes of cubic graphs are obtained.}
}