On signless and normalized Laplacian spectra of a subgraph of the total graph of Zn

<p>In this paper, we study the signless Laplacian eigenvalues of the subgraph <span class="math inline">\(Z^*(\Gamma(\mathbb{Z}_n))\)</span> of the total graph of the integers modulo <span class="math inline">\(n\)</span>, <span class="math inline">\(\mathbb{Z}_n\)</span>, for certain values of <span class="math inline">\(n\)</span>. We also identify specific values of <span class="math inline">\(n\)</span> for which the graph is <span class="math inline">\(Q\)</span>-integral. Finally, we discuss the normalized Laplacian spectrum of <span class="math inline">\(Z^*(\Gamma(\mathbb{Z}_n))\)</span>.</p>