Table 1 Chain instability inertias of different topological structures.

From: Structural importance analysis and key chambers identification for chain instability of chamber group in coal mine

Patterns

Topological structures

Number of chambers

Instability inertia

Total

Important chamber

General chamber

Individual chamber

I

1

Two-chamber group

II

2

2

0

1

III

2

0

2

0

Three-chamber group

IV

3

3

0

1

V

3

1

2

0.33

VI

3

0

3

0

Four-chamber group

VII

4

4

0

1

VIII

4

2

2

0.50

IX

4

1

3

0.25

X

4

0

4

0

……

n-chamber group

\(\frac{n(n - 1)}{2}\)

n

n

0

1

……

\(\frac{n(n - 1)}{2} + {\text{i}}\)

n

m

n-m

m/n

……

\(\frac{n(n + 1)}{2}\)

n

0

n

0