TY - JOUR T1 - On the Gracefulness of Graph $(jC_{4n}) ∪ P_m$ AU - Zhang , Zhishang AU - Zhang , Qingcheng AU - Wang , Chunyue JO - Communications in Mathematical Research VL - 2 SP - 139 EP - 146 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19096.html KW - graceful labeling, graceful graph, path, cycle, disjoint union. AB -

The present paper deals with the gracefulness of unconnected graph $(jC_{4n}) ∪ P_m$, and proves the following result: for positive integers $n$, $j$ and $m$ with $n ≥ 1$, $j ≥ 2$, the unconnected graph $(jC_{4n}) ∪ P_m$ is a graceful graph for $m = j − 1$ or $m ≥ n + j$, where $C_{4n}$ is a cycle with $4n$ vertexes, $P_m$ is a path with $m + 1$ vertexes, and $(jC_{4n}) ∪ P_m$ denotes the disjoint union of $j − C_{4n}$ and $P_m$.