Hilbert-Samuel Multiplicity of a Bipartite Graph
  Let $G$ be a bipartite graph and $I(G)$ the toric ideal associated to the graph $G$. In this article we calculate Hilbert-Samuel multiplicity of the graph $G$ for which the toric ideal $I(G)$ is generated by a quadratic binomials and it satiesfies some conditions. 
Priya Das, Himadri Mukherjee
math.AC