Geodesic
The $\circ $ operation and $*$ operation of Cohen-Macaulay bipartite graphs
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 735-757
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Let $G$ be a finite simple graph with the vertex set $V$ and let $I_G$ be its edge ideal in the polynomial ring $S= \mathbb {K} [V]$. We compute the depth and the Castelnuovo-Mumford regularity of $S/I_G$ when $G=G_1\circ G_2$ or $G=G_1* G_2$ is a graph obtained from Cohen-Macaulay bipartite graphs $G_1$, $G_2$ by the $\circ $ operation or $*$ operation, respectively.
Let $G$ be a finite simple graph with the vertex set $V$ and let $I_G$ be its edge ideal in the polynomial ring $S= \mathbb {K} [V]$. We compute the depth and the Castelnuovo-Mumford regularity of $S/I_G$ when $G=G_1\circ G_2$ or $G=G_1* G_2$ is a graph obtained from Cohen-Macaulay bipartite graphs $G_1$, $G_2$ by the $\circ $ operation or $*$ operation, respectively.
DOI : 10.21136/CMJ.2024.0438-23
Classification : 05E40, 13A15, 13C15, 13D02
Keywords: regularity; depth; $\circ $ operation; $*$ operation; Cohen-Macaulay bipartite graph 
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     title = {The $\circ $ operation and $*$ operation of {Cohen-Macaulay} bipartite graphs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {735--757},
     year = {2024},
     volume = {74},
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Yang, Yulong; Zhu, Guangjun; Cui, Yijun; Duan, Shiya. The $\circ $ operation and $*$ operation of Cohen-Macaulay bipartite graphs. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 735-757. doi: 10.21136/CMJ.2024.0438-23

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