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arXiv · 1612.03544

Linear Residuals and Gallai-Simplicial Complexes

Imran Anwar·Zunaira Kosar·Shaheen Nazir·Khurram Shabbir
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Abstract

In this paper, we give a new algebraic criterion for the {\em shellability} of (non-pure) simplicial complex $\Delta$ over $[n]$, shellable in the sense of Bj\"orner and Wachs \cite{BW}. We show that the spanning simplicial complex of doubly uni-cyclic graph is non-pure shellable. Moreover, we introduce the concept of Gallai-simplicial complex $\Delta_{\Gamma}(G)$ of a finite simple graph $G$. We applied the obtained criterion to discuss the shellability of Gallai simplicial complexes associated to various classes of graphs..

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Imran Anwar, Zunaira Kosar, Shaheen Nazir, Khurram Shabbir. 2016-12-12. Linear Residuals and Gallai-Simplicial Complexes. https://arxiv.org/abs/1612.03544

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