آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 111 |
| تعداد مقالات | 1,247 |
| تعداد مشاهده مقاله | 1,199,575 |
| تعداد دریافت فایل اصل مقاله | 1,060,297 |
Some families of $\alpha$-labeled subgraphs of the integral grid | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 7، دوره 8، شماره 1، خرداد 2023، صفحه 77-101 اصل مقاله (622.33 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.26989.1175 | ||
| نویسندگان | ||
| Christian Barrientos* 1؛ Sarah Minion2 | ||
| 1Department of Mathematics Valencia College Orlando, FL 32832 United States | ||
| 2Department of Mathematics Full Sail University Orlando, FL 32792 United States | ||
| چکیده | ||
| In this work we study the most restrictive variety of graceful labelings, that is, we study the existence of an $\alpha$-labeling for some families of graphs that can be embedded in the integral grid. Among the categories of graphs considered here we have a subfamily of 2-link fences, a subfamily of column-convex polyominoes, and a subfamily of irregular cyclic-snakes. We prove that under some conditions, the a-labelings of these graphs can be transformed into harmonious labelings. We also present a closed formula for the number of 2-link fences examined here. | ||
| کلیدواژه‌ها | ||
| graceful؛ α-labeling؛ harmonious؛ polyomino؛ fence | ||
| مراجع | ||
|
[1] B. D. Acharya, Are all polyominoes arbitrarily graceful?, Proc. First Southeast Asian Graph Theory Colloquium, Ed. K. M. Koh and H. P. Yap, Springer-Verlag, N. Y., 34 (1984), 205–211.
[2] C. Barrientos, Graceful labelings of chain and corona graphs, Bull. Inst. Combin. Appl. 34 (2002), 17–26.
[3] C. Barrientos and S. Minion, Alpha labelings of snake polyominoes and hexagonal chains, Bull. Inst. Combin. Appl. 74 (2015), 73–83.
[4] C. Barrientos and S. Minion, Counting and labeling grid related graphs, Electron. J. Graph Theory Appl. 7 (2019), no. 2, 349–363.
[5] G. Chartrand and L. Lesniak, Graphs & digraphs, 4th ed., CRC Press, Boca Raton, 2005.
[6] R. Figueroa-Centeno, R. Ichishima, and F. Muntaner-Batle, On edge-magic labelings of certain disjoint unions of graphs, Australas. J. Combin. 32 (2005), 225–242.
[7] J. A. Gallian, A survey: recent results, conjectures and open problems on labeling graphs, J. Graph Theory 13 (1989), 491–504.
[8] , A dynamic survey of graph labeling, Electron. J. Combin. (2020).
[9] S. W. Golomb, Polyominoes: Puzzles, patterns, problems, and packings, Princeton University Press, 1996.
[10] R. L. Graham and N. J. A. Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Discrete Methods, 1 (1980), 382–404.
[11] D. Jungreis and M. Reid, Labeling grids, Ars Combin. 34 (1992), 167–182.
[12] S. C. López and F. A. Muntaner-Batle, Graceful, harmonious and magic type labelings: Relations and techniques, Springer, Cham, 2017.
[13] M. Maheo and H. Thuillier, On d-graceful graphs, Ars Combin. 13 (1982), 181–192.
[14] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach (1967), 349–355.
[15] , Labelling snakes, Ars Combin. 3 (1977), 67–74.
[16] A. Rosa and J. Širáň, Bipartite labelings of trees and the gracesize, J. Graph Theory 19 (1995), 201–215.
[17] P. J. Slater, On k-graceful graphs, Proc. of the 13th S.E. Conf. on Combinatorics, Graph Theory and Computing (1982), 53–57. | ||
|
آمار تعداد مشاهده مقاله: 425 تعداد دریافت فایل اصل مقاله: 713 |
||