Some Properties on the Harmonic Index of Molecular Trees

Table 1

Nine classes of molecular trees and 𝜑(𝑇)<72/420.

Set	𝑛2	𝑛3	Nonzero 𝑥^′𝑖𝑗𝑠 value	𝜑(𝑇)	𝑘	𝑛
ℳ1𝑇(𝑛)	0	0		0	2	𝑛≥5
ℳ2𝑇(𝑛)	0	1	𝑥34=3	24/420	1	𝑛≥13
ℳ3𝑇(𝑛)	1	0	𝑥24=2	28/420	0	𝑛≥9
ℳ4𝑇(𝑛)	0	2	𝑥34=6	48/420	0	𝑛≥21
ℳ5𝑇(𝑛)	0	1	𝑥34=2,𝑥13=1	51/420	1	𝑛≥10
ℳ6𝑇(𝑛)	0	2	𝑥34=4,𝑥33=1	53/420	0	𝑛≥18
ℳ7𝑇(𝑛)	1	1	𝑥24=2,𝑥34=3	52/420	2	𝑛≥17
ℳ8𝑇(𝑛)	2	0	𝑥24=4	56/420	1	𝑛≥13
ℳ9𝑇(𝑛)	1	1	𝑥24=1,𝑥34=2,𝑥23=1	65/420	2	𝑛≥14