Geodesic
On \(m\)-closed graphs
Leila Sharifan1 ; Masoumeh Javanbakht1
1Hakim Sabzevari University
The electronic journal of combinatorics, Tome 21 (2014) no. 4
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A graph is closed when its vertices have a labeling by $[n]$ such that the binomial edge ideal $J_G$ has a quadratic Gröbner basis with respect to the lexicographic order induced by $x_1 > \ldots > x_n > y_1> \ldots > y_n$. In this paper, we generalize this notion and study the so called $m$-closed graphs. We find equivalent condition to $3$-closed property of an arbitrary tree $T$. Using it, we classify a class of $3$-closed trees. The primary decomposition of this class of graphs is also studied.
DOI : 10.37236/4406
Classification : 05C78, 05C25, 13P10, 05E40
Mots-clés : \(m\)-closed graph, binomial edge ideal, reduced Gröbner basis, admissible path

Leila Sharifan  1   ; Masoumeh Javanbakht  1

1 Hakim Sabzevari University 
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     title = {On \(m\)-closed graphs},
     journal = {The electronic journal of combinatorics},
     year = {2014},
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Leila Sharifan; Masoumeh Javanbakht. On \(m\)-closed graphs. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4406

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