Hajisharifi, N., Tehranian, A. (2016). A new construction for vertex decomposable graphs. Transactions on Combinatorics, 5(3), 33-38. doi: 10.22108/toc.2016.13316

Nasser Hajisharifi; Abolfazl Tehranian. "A new construction for vertex decomposable graphs". Transactions on Combinatorics, 5, 3, 2016, 33-38. doi: 10.22108/toc.2016.13316

Hajisharifi, N., Tehranian, A. (2016). 'A new construction for vertex decomposable graphs', Transactions on Combinatorics, 5(3), pp. 33-38. doi: 10.22108/toc.2016.13316

Hajisharifi, N., Tehranian, A. A new construction for vertex decomposable graphs. Transactions on Combinatorics, 2016; 5(3): 33-38. doi: 10.22108/toc.2016.13316

^{1}Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran

^{2}Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Abstract

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.

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