Table 5 All types of edge-cuts with their cardinalities.

From: On Zagreb coindices and Mostar index of \(TiO_2\) nanotubes

Case

Cut-type

Number of cuts

Size of cuts

When \(m>n\)

\(A_i\)

\(1\le i\le n\)

4i

\(B_i\)

\(1\le i\le m-n-1\)

4n

\(C_i\)

\(1\le i\le n\)

\(2(2i-1)\)

\(Y_i\)

\(1\le i\le n\)

2m

\(Z_i\)

\(1\le i\le 2n-1\)

2m

When \(m\le n\)

\(A_i\)

\(1\le i\le m-1\)

\(4(4i-2)\)

\(B_i\)

\(1\le i\le n-m+1\)

\(4(m-1)+2\)

\(C_i\)

\(1\le i\le m-1\)

\(2(2i-1)\)

\(Y_i\)

\(1\le i\le n\)

2m

\(Z_i\)

\(1\le i\le 2n-1\)

2m