Some Graceful Graphs

Abstract

We have investigated some general classes of disconnected graceful graphs. We obtain the graceful labeling for $(P_{m} \times P_{n})~\bigcup~(P_{r} \times P_{s})$,~$C_{2f+3}~\bigcup~(P_{m} \times P_{n})~\bigcup~(P_{r} \times P_{s})$, where $ m,~n,~ r, ~s \in N - \{1\} $ and $f= 2(mn + rs) - (m + n + r + s)$. We also show that the tensor product of $P_{n}$ and $P_{3}$, where $n \in N - \{1,~2 \}$ admits graceful labeling. In addition to this we prove that a graph called star of cycle $C^{\star}_{n}$ is graceful, for $n \equiv 0$ (mod $4$).