Abstract
The PI-index of a graph \(G\) is defined by \(\mathrm{PI}(G)=\sum_{e=uv\in E}(m_u(e)+m_v(e))\), where \(m_u(e)\) is the number of edges in \(G\) lying closer to the vertex \(u\) than to the vertex \(v\). In this paper, using probabilistic method we disprove
a conjecture about the PI-index posed by Khalifeh et al. [Order of Magnitude of the PI index, MATCH Commun. Math. Comput. Chem. 65 (2011) 51--56].
