Geodesic
Vertex Decomposable Graph
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 203 .

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Let $G$ be a simple graph on the vertex set $V(G)$ and $S=\{x_{11},\ldots,x_{n1}\}$ a subset of $V(G)$. Let $m_1,\ldots,m_n\geq 2$ be integers and $G_1,\ldots,G_n$ connected simple graphs on the vertex sets $V(G_i)=\{x_{i1},\ldots,x_{im_i}\}$ for $i=1,\ldots,n$. The graph $G(G_1,\ldots,G_n)$ is obtained from $G$ by attaching $G_i$ to $G$ at the vertex $x_{i1}$ for $i=1,\ldots,n$. We give a characterization of $G(G_1,\ldots,G_n)$ for being vertex decomposable. This generalizes a result due to Mousivand, Seyed Fakhari, and Yassemi.
DOI : 10.2298/PIM1613203H
Classification : 13F55, 05E40 05C70, 05C38
Keywords: vertex decomposable, Cohen--Macaulay 
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     title = {Vertex {Decomposable} {Graph}},
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     pages = {203 },
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N. Hajisharifi; S. Yassemi. Vertex Decomposable Graph. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 203 . doi : 10.2298/PIM1613203H. http://geodesic.mathdoc.fr/articles/10.2298/PIM1613203H/

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