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

The chemical graphs are graphs that have no vertex with degree greater than 4. The sigma index of a graph \(G\) is defined by \(∑uv∈ E(G) (degG(u)-degG(v))²\), where \(degG(u)\) stands for the degree of vertex \(u\) in \(G\). 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 \(n\) having \(m\) edges and \(p\) pendent vertices.