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

Zhishang Zhang, Qingcheng Zhang & Chunyue Wang

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.

  • AMS Subject Headings

05C78

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-139, author = {Zhishang and Zhang and and 18376 and and Zhishang Zhang and Qingcheng and Zhang and and 18377 and and Qingcheng Zhang and Chunyue and Wang and and 18378 and and Chunyue Wang}, 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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