Year 2019, Volume 2, Issue 1, Pages 1 - 10 2019-03-20

Special Graceful Labelings of Irregular Fences and Lobsters

Christian Barrientos [1]

68 132

Irregular fences are subgraphs of $P_m \times P_n$ formed with $m$ copies of $P_n$ in such a way that two consecutive copies of $P_n$ are connected with one or two edges; if two edges are used, then they are located in levels separated an odd number of units. We prove here that any of these fences admits a special kind of graceful labeling, called $\alpha$-labeling. We show that there is a huge variety of this type of fences presenting a closed formula to determine the number of them that can be built on the grid $[1,m] \times [1, n]$. If only one edge is used to connect any pair of consecutive copies of $P_n$, the resulting graph is a tree. We use the $\alpha$-labelings of this type of fences to construct and label a subfamily of lobsters, partially answering the long standing conjecture of Bermond that states that all lobsters are graceful. The final labeling of the lobsters presented here is not only graceful, it is an $\alpha$-labeling, therefore they can be used to produce new graceful trees.
Fence, Graceful labelling, Lobster
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Primary Language en
Subjects Mathematics
Journal Section Articles
Authors

Orcid: 0000-0003-2838-8687
Author: Christian Barrientos (Primary Author)
Institution: Valencia College
Country: United States


Bibtex @research article { ujma520682, journal = {Universal Journal of Mathematics and Applications}, issn = {2619-9653}, address = {Emrah Evren KARA}, year = {2019}, volume = {2}, pages = {1 - 10}, doi = {10.32323/ujma.520682}, title = {Special Graceful Labelings of Irregular Fences and Lobsters}, key = {cite}, author = {Barrientos, Christian} }
APA Barrientos, C . (2019). Special Graceful Labelings of Irregular Fences and Lobsters. Universal Journal of Mathematics and Applications, 2 (1), 1-10. DOI: 10.32323/ujma.520682
MLA Barrientos, C . "Special Graceful Labelings of Irregular Fences and Lobsters". Universal Journal of Mathematics and Applications 2 (2019): 1-10 <http://dergipark.org.tr/ujma/issue/44032/520682>
Chicago Barrientos, C . "Special Graceful Labelings of Irregular Fences and Lobsters". Universal Journal of Mathematics and Applications 2 (2019): 1-10
RIS TY - JOUR T1 - Special Graceful Labelings of Irregular Fences and Lobsters AU - Christian Barrientos Y1 - 2019 PY - 2019 N1 - doi: 10.32323/ujma.520682 DO - 10.32323/ujma.520682 T2 - Universal Journal of Mathematics and Applications JF - Journal JO - JOR SP - 1 EP - 10 VL - 2 IS - 1 SN - 2619-9653- M3 - doi: 10.32323/ujma.520682 UR - https://doi.org/10.32323/ujma.520682 Y2 - 2019 ER -
EndNote %0 Universal Journal of Mathematics and Applications Special Graceful Labelings of Irregular Fences and Lobsters %A Christian Barrientos %T Special Graceful Labelings of Irregular Fences and Lobsters %D 2019 %J Universal Journal of Mathematics and Applications %P 2619-9653- %V 2 %N 1 %R doi: 10.32323/ujma.520682 %U 10.32323/ujma.520682
ISNAD Barrientos, Christian . "Special Graceful Labelings of Irregular Fences and Lobsters". Universal Journal of Mathematics and Applications 2 / 1 (March 2019): 1-10. https://doi.org/10.32323/ujma.520682