@article{Bilal_Ahmed_Mahmood_Binyamin_2022, place={Sofia, Bulgaria}, title={The NF-Number of Two Complete Graphs Joined by a Common Vertex}, volume={75}, url={https://proceedings.bas.bg/index.php/cr/article/view/75}, DOI={10.7546/CRABS.2022.05.02}, abstractNote={<p>Let $$\Delta$$ be a simplicial complex on the vertex set $$V$$. For $$m=1,2,3,\dots$$, the notion of $$m$$-th $$\mathcal{NF}$$-complex of $$\Delta$$, $$\delta^{(m)}_{\mathcal{NF }(\Delta)$$, was introduced by Hibi and Mahmood in [5], where $$\delta^{(m)}_{\mathcal{NF }(\Delta)=\delta_{\mathcal{NF }(\delta^{(m-1)}_{\mathcal{NF }(\Delta))$$ with setting $$\delta^{(1)}_{\mathcal{NF }(\Delta)=\delta_{\mathcal{NF }(\Delta)$$ such that $$\delta_{\mathcal{NF }(\Delta)$$ is the Stanley–Reisner complex of the facet ideal of $$\Delta$$. The $$\mathcal{NF}$$-number of $$\Delta$$ is the least positive integer $$q$$ for which $$\delta^{(q)}_{\mathcal{NF }(\Delta)\simeq\Delta$$.</p>
<p>In this paper, we investigated the $$\mathcal{NF}$$-number of two copies of complete graphs $$K_n$$ joined by one common vertex $$\{u\}$$. At the end, we also provided an explicit example for the case of two copies of $$K_5$$ joined by common vertex $$\{u\}$$.</p>}, number={5}, journal={Proceedings of the Bulgarian Academy of Sciences}, author={Bilal, Hafiz and Ahmed, Sarfraz and Mahmood, Hasan and Binyamin, Muhammad}, year={2022}, month={May}, pages={640–648} }