TY - JOUR
ID - 13316
TI - A new construction for vertex decomposable graphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Hajisharifi, Nasser
AU - Tehranian, Abolfazl
AD - Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran
AD - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Y1 - 2016
PY - 2016
VL - 5
IS - 3
SP - 33
EP - 38
KW - vertex decomposable
KW - shellabel
KW - Cohen-Macaulay
DO - 10.22108/toc.2016.13316
N2 - Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $S \subseteq V(G)$. Adding a whisker to $G$ at $x$ means adding a new vertex $y$ and edge $xy$ to $G$ where $x \in V(G)$. The graph $G\cup W(S)$ is obtained from $G$ by adding a whisker to every vertex of $S$. We prove that if $G\setminus S$ is either a graph with no chordless cycle of length other than $3$ or $5$, chordal graph or $C_5$, then $G \cup W(S)$ is a vertex decomposable graph.
UR - https://toc.ui.ac.ir/article_13316.html
L1 - https://toc.ui.ac.ir/article_13316_43779a03b5b9504e38c712a31b3b66d0.pdf
ER -