Abstract   Let   G   be a undirected graph without loops and multiple edges. By   η   (  G  )   ,    θ   (  G  )    and   p   (  G  )    we respectively denote the nullity, the dimension of cycle space, and the number of pendant vertices of   G  . If each component of   G   contains at least two vertices, then it is proved that   η   (  G  )   ≤  2  θ   (  G  )   +  p   (  G  )   , the equality is attained if and only if every component of   G   is a cycle with size a multiple of   4  .
['Xiaobin Ma', 'Dein Wong', 'Fenglei Tian']
Nullity of a graph in terms of the dimension of cycle space and the number of pendant vertices