@Article{CMR-27-139,
author = {Zhang , ZhishangZhang , Qingcheng and Wang , Chunyue},
title = {On the Gracefulness of Graph $(jC_{4n}) ∪ P_m$},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {27},
number = {2},
pages = {139--146},
abstract = {<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>},
issn = {2707-8523},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cmr/19096.html}
}