Graphs that minimizing max–min rodeg index

Abstract

The max–min rodeg (${M\!m_{sde}}$) index is a useful topological index in mathematical chemistry. Damir Vuki$\check{\text {c}}$evi$\acute{\text {c}}$ studied the mathematical properties of the max–min rodeg index. In this paper, we determine the n-vertex trees with the second, the third and the fourth for $n\ge 7$, and the fifth for $n\ge 10$ minimum $M\!m_{sde}$ indices, unicyclic graphs with the second and the third for $n\ge 5$, the fourth, the fifth and the sixth for $n\ge 7$, and the seventh for $n\ge 9$ minimum $M\!m_{sde}$ indices, and bicyclic graphs with the first for $n\ge 4$, the second and the third for $n\ge 6$, and the fourth for $n\ge 8$ minimum $M\!m_{sde}$ indices.