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چکیده
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Let $R=k[x_1,\ldots,x_n]$ be the polynomial ring over a field $k$, $G$ be a graph on vertex set $V=\{x_1,\dots,x_n\}$ and $I=I(G)$ be its edge ideal. In this paper we study bi-sequentially Cohen-Macaulay bipartite graphs and as consequence we classify all bi-sequentially Cohen-Macaulay tree graphs. Furthermore, if $R/I$ is bi-sequentially Cohen-Macaulay then we determine the projective dimension of $R/I$. Moreover, we give some examples.
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