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 - <p style="text-align: justify;">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 $P_m$.</p>