On the sigma index of chemical graphs with a given order, number of edges and pendent vertices

<p>The chemical graphs are graphs that have no vertex with degree greater than 4. The sigma index of a graph <span class="math inline">\(G\)</span> is defined by <span class="math inline">\(\sum_{uv\in E(G)} (deg_{G}(u)-deg_{G}(v))^{2}\)</span>, where <span class="math inline">\(deg_{G}(u)\)</span> stands for the degree of vertex <span class="math inline">\(u\)</span> in <span class="math inline">\(G\)</span>. In this work, we present lower and upper bounds on the sigma index for chemical trees with a given order and number of pendent vertices. Furthermore, we solve the problem of minimizing sigma index for chemical graphs of order <span class="math inline">\(n\)</span> having <span class="math inline">\(m\)</span> edges and <span class="math inline">\(p\)</span> pendent vertices.</p>