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Year 2019, Volume: 2 Issue: 2, 114 - 120, 27.06.2019
https://doi.org/10.33434/cams.505485

Abstract

References

  • [1] A. Rosa, J. Siran, Bipartite labelings of trees and the gracesize, J. Graph Theory, 19 (1995), 201-215.
  • [2] M. Maheo, H. Thuillier, On d-graceful graphs, Ars Combin., 13 (1982), 181-192.
  • [3] P. J. Slater, On k-graceful graphs, Proceedings of the 13th Southeastern International Conference on Combinatorics, Graph Theory and Computing, (1982), 53-57.
  • [4] C. Barrientos, Graceful labelings of chain and corona graphs, Bull. Inst. Combin. Appl., 34 (2002), 17-26.
  • [5] C. Barrientos, S. Minion, Alpha labelings of snake polyominoes and hexagonal chains, Bull. Inst. Combin. Appl., 74 (2015), 73-83.
  • [6] G. Chartrand, L. Lesniak, Graphs & Digraphs, 2nd ed. Wadsworth & Brooks/Cole, 1986.
  • [7] J. A. Gallian, A dynamic survey of graph labeling, Electronic J. Combin., 21(#DS6), 2018.
  • [8] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (International Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967), 349-355.
  • [9] J.-F. Sloane, https://oeis.org/A277504, 2016.
  • [10] B. D. Acharya, M. K. Gill, On the index of gracefulness of a graph and the gracefulness of two-dimensional square lattice graphs, Indian J. Math., 23 (1981), 81-94.
  • [11] K. Kathiresan, Subvisions of ladders are graceful, Indian J. Pure Appl. Math., 23 (1992), 21-23.

The Graceful Coalescence of Alpha Cycles

Year 2019, Volume: 2 Issue: 2, 114 - 120, 27.06.2019
https://doi.org/10.33434/cams.505485

Abstract


The standard coalescence of two graphs is extended, allowing to identify two isomorphic subgraphs instead of a single vertex. It is proven here that any succesive coalescence of cycles of size $n$, where $n$ is divisible by four, results in an $\alpha$-graph, that is, the most restrictive kind of graceful graph, when the subgraphs identified are paths of sizes not exceeding $\frac{n}{2}$. Using the coalescence and another similar technique, it is proven that some subdivisions of the ladder $L_n = P_2 \times P_n$ also admit an $\alpha$-labeling, extending and generalizing the existing results for this type of subdivided graphs.

References

  • [1] A. Rosa, J. Siran, Bipartite labelings of trees and the gracesize, J. Graph Theory, 19 (1995), 201-215.
  • [2] M. Maheo, H. Thuillier, On d-graceful graphs, Ars Combin., 13 (1982), 181-192.
  • [3] P. J. Slater, On k-graceful graphs, Proceedings of the 13th Southeastern International Conference on Combinatorics, Graph Theory and Computing, (1982), 53-57.
  • [4] C. Barrientos, Graceful labelings of chain and corona graphs, Bull. Inst. Combin. Appl., 34 (2002), 17-26.
  • [5] C. Barrientos, S. Minion, Alpha labelings of snake polyominoes and hexagonal chains, Bull. Inst. Combin. Appl., 74 (2015), 73-83.
  • [6] G. Chartrand, L. Lesniak, Graphs & Digraphs, 2nd ed. Wadsworth & Brooks/Cole, 1986.
  • [7] J. A. Gallian, A dynamic survey of graph labeling, Electronic J. Combin., 21(#DS6), 2018.
  • [8] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (International Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967), 349-355.
  • [9] J.-F. Sloane, https://oeis.org/A277504, 2016.
  • [10] B. D. Acharya, M. K. Gill, On the index of gracefulness of a graph and the gracefulness of two-dimensional square lattice graphs, Indian J. Math., 23 (1981), 81-94.
  • [11] K. Kathiresan, Subvisions of ladders are graceful, Indian J. Pure Appl. Math., 23 (1992), 21-23.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Christian Barrientos 0000-0003-2838-8687

Sarah Minion This is me 0000-0002-8523-3369

Publication Date June 27, 2019
Submission Date December 30, 2018
Acceptance Date February 21, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Barrientos, C., & Minion, S. (2019). The Graceful Coalescence of Alpha Cycles. Communications in Advanced Mathematical Sciences, 2(2), 114-120. https://doi.org/10.33434/cams.505485
AMA Barrientos C, Minion S. The Graceful Coalescence of Alpha Cycles. Communications in Advanced Mathematical Sciences. June 2019;2(2):114-120. doi:10.33434/cams.505485
Chicago Barrientos, Christian, and Sarah Minion. “The Graceful Coalescence of Alpha Cycles”. Communications in Advanced Mathematical Sciences 2, no. 2 (June 2019): 114-20. https://doi.org/10.33434/cams.505485.
EndNote Barrientos C, Minion S (June 1, 2019) The Graceful Coalescence of Alpha Cycles. Communications in Advanced Mathematical Sciences 2 2 114–120.
IEEE C. Barrientos and S. Minion, “The Graceful Coalescence of Alpha Cycles”, Communications in Advanced Mathematical Sciences, vol. 2, no. 2, pp. 114–120, 2019, doi: 10.33434/cams.505485.
ISNAD Barrientos, Christian - Minion, Sarah. “The Graceful Coalescence of Alpha Cycles”. Communications in Advanced Mathematical Sciences 2/2 (June 2019), 114-120. https://doi.org/10.33434/cams.505485.
JAMA Barrientos C, Minion S. The Graceful Coalescence of Alpha Cycles. Communications in Advanced Mathematical Sciences. 2019;2:114–120.
MLA Barrientos, Christian and Sarah Minion. “The Graceful Coalescence of Alpha Cycles”. Communications in Advanced Mathematical Sciences, vol. 2, no. 2, 2019, pp. 114-20, doi:10.33434/cams.505485.
Vancouver Barrientos C, Minion S. The Graceful Coalescence of Alpha Cycles. Communications in Advanced Mathematical Sciences. 2019;2(2):114-20.

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