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The  h -vectors of homogeneous rings are one of the most important invariants that often reflect ring-theoretic properties. On the other hand, there are a few examples of edge rings of graphs whose  h -vectors are explicitly computed. In this paper, we compute the  h -vector of a special family of graphs, by using the technique of initial ideals and the associated simplicial complex.

The h -vectors of the edge rings of a special family of graphs