Extremal phenylene chains with respect to detour indices

Abstract

Computing topological indices of molecular structures is a fundamental and classical topic. In organic chemistry, hexagonal and quadrilateral molecular structures are very common. The detour index $$\omega (G)$$ of a connected graph G is defined as $$\omega (G)=\sum \nolimits _{\{u,v\}\subseteq V(G)}l_{G}(u,v)$$ , where $$l_{G}(u,v)$$ denotes the detour distance between vertices u and v. In this study, we obtain the explicit analytical expression for detour index of phenylene chains with a fixed number of hexagons. Further minimal and maximal phenylene chains are obtained.