Volume 27, Issue 2
On the Gracefulness of Graph $(jC_{4n}) ∪ P_m$

Commun. Math. Res., 27 (2011), pp. 139-146.

Published online: 2021-05

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• Abstract

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 $P_m$.

• Keywords

graceful labeling, graceful graph, path, cycle, disjoint union.

05C78

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@Article{CMR-27-139, author = {Zhang , Zhishang and Zhang , 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 = {

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 $P_m$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19096.html} }
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 $P_m$.

Zhishang Zhang, Qingcheng Zhang & Chunyue Wang. (2021). On the Gracefulness of Graph $(jC_{4n}) ∪ P_m$. Communications in Mathematical Research . 27 (2). 139-146. doi:
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