Skip to main content

Table 2 Zumkeller numbers used to label the edges of \(SSD(C_{m}\times P_{n})\)

From: k-Zumkeller labeling of super subdivision of some graphs

Edges Num. of edges Labels Num. of labels
\(u_{ij}u_{i,j(j+1)}^{k}\),
\(u_{in}u_{i,n1}^{k}\)
\(1\le i\le m\),
\(1\le j\le n-1\)
mnt \(p2^{(2mn-1)t-nti+k}\) mt
\(u_{i,j(j+1)}^{k}u_{i(j+1)}\)
\(1\le i\le m\),
\(1\le j\le n-1\)
\(u_{(i-1)j}u_{(i-1)i,j}^{k}\)
\(2\le i\le m\),
\(2\le j\le n-1\)
\(u_{(i-1),n1}^{k}u_{(i-1)1}\),
\(2\le i\le m\)
\(u_{i(i+1),j}^{k}u_{(i+1)j}\)
\(1\le i\le m\),
\(2\le j\le n-1\)
\(u_{(i-2)1}u_{(i-2)(i-1),1}^{k}\)
\(3\le i\le m\),
\(1\le j\le n-1\)
\(u_{(i-1)i,1}^{k}u_{i1}\),
\(2\le i\le m\)
\((n-1)mt\)
\((n-1)(m-1)t\)
\((m-1)t\)
\((m-1)t\)
\((m-2)t\)
\((m-1)t\)
\(p2^{2mnt-nti+k }\) mt
\(u_{m,n1}^{k}u_{m1}\),
\(u_{(m-1)1}u_{(m-1)m,1}^{k}\)
2t \(p2^{mnt-nt+k}\) t