Table 1 Zumkeller numbers used to label the edges of \(SSD(P_{m}\times P_{n})\)
From: k-Zumkeller labeling of super subdivision of some graphs
Edges | Labels | Num. of labels |
|---|---|---|
\(u_{1j}u_{1,j(j+1)}^{k}\) | \(p2^{(2mn-m-n-1)t+k}\) | \((n-1)t\) |
\(u_{ij}u_{i,j(j+1)}^{k}\), \(u_{(i-1)j}u_{(i-1)i,j}^{k}\), \(2\le i\le m\) | \(p2^{(2mn-m-1)t-(n-1)ti+k}\) | \((m-1)(n-1)t\) |
\(u_{i,j(j+1)}^{k}u_{i(j+1)}\), \(u_{i(i+1),j}^{k}u_{(i+1)j}\), \(1\le i\le m-1\) | \(p2^{(2mn-m-1)t-(n-1)ti+k}\) | \((m-1)(n-1)t\) |
\(u_{m,j(j+1)}^{k}u_{m(j+1)}\) | \(p2^{(mn-1)t+k}\) | \((n-1)t\) |