A classification of polyhedral graph by combinatorially rigid vertices
  When the number of non-triangular faces adjacent to a vertex $v$ is less than or equal to three, the vertex $v$ will be called (\emph{combinatorially}) \emph{rigid}.   We study the number of rigid vertices and suggest a conjecture on a classification of polyhedra. 
Seonhwa Kim, Yunhi Cho
math.MG math.CO