آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 126 |
| تعداد مقالات | 1,601 |
| تعداد مشاهده مقاله | 1,813,360 |
| تعداد دریافت فایل اصل مقاله | 1,684,555 |
Some Results on Local Distance Antimagic Chromatic Number of Graphs* | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 05 تیر 1405 اصل مقاله (528.83 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31314.2818 | ||
| نویسندگان | ||
| Maurice Genevieva Almeida* 1، 2؛ Tarkeshwar Singh1 | ||
| 1Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Goa, India | ||
| 2Rosary College of Commerce and Arts, Navelim, Salcete-Goa, India | ||
| چکیده | ||
| Let G = (V,E) be a simple graph of order n without isolated vertices. A bijection f : V →{1,2,...,n} is called a local distance antimagic labeling if w(u) is not equal to w(v) for every edge uv of G, where w(u) is the sum of the labels of neighbors of vertex u. The local distance antimagic chromatic number of a graph χld(G) is defined as the minimum number of colors taken over all the colorings of G induced by local distance antimagic labeling of G. In this paper, we study the local distance antimagic chromatic number for the join of graphs and the lexicographic product of graphs with the complement of the complete graph. | ||
| کلیدواژهها | ||
| Local distance antimagic labeling؛ local distance antimagic chromatic number؛ lexicographic product | ||
| مراجع | ||
|
[1] S. Arumugam, K. Premalatha, M. Bača, and A. Semaničová-Feňovčíková, Local antimagic vertex coloring of a graphs, Graphs Combin. 33 (2017), no. 2, 275–285. https://doi.org/10.1007/s00373-017-1758-7
[2] J. Bensmail, M. Senhaji, and K.S. Lyngsie, On a combination of the 1-2-3 conjecture and the antimagic labeling conjecture, Discrete Mathematics and Theoretical Computer Science 19 (2017), no. 1, 21. https://doi.org/10.23638/DMTCS-19-1-21
[3] G. Chartrand and L. Lesniak, Graphs and Digraphs, Chapman and Hall, CRC, 2012.
[4] T. Divya and S. Yamini, Local distance antimagic vertex coloring of graphs, 2021. https://doi.org/10.48550/arXiv.2106.01833
[5] D. Geller and S. Stahl, The chromatic number and other parameters of the lexicographic product, J. Combin. Theory Ser. B 19 (1975), no. 1, 87–95. https://doi.org/10.1016/0095-8956(75)90076-3
[6] A.K. Handa, Studies in distance antimagic graphs, Ph.D. thesis, Birla Institute of Technology and Science, K.K. Birla Goa Campus, Goa, India, 2021.
[7] A.K. Handa, A. Godinho, and T. Singh, On local distance antimagic labeling of graphs, AKCE Int. J. Graphs Comb. 21 (2024), no. 1, 91–96. https://doi.org/10.1080/09728600.2023.2256811
[8] T. Harmuth, Ueber magische Quadrate und ahnliche Zahlenfiguren, Arch. Math. Phys. 66 (1881), 286–313.
[9] T. Harmuth, Ueber magische Rechtecke mit ungraden Seitenzahlen, Arch. Math. Phys. 66 (1881), 413–447.
[10] N. Hartsfield and G. Ringel, Pearls in Graph Theory, Academic Press, San Diego, 1990.
[11] J. Haslegrave, Proof of a local antimagic conjecture, Discrete Math. Theoretical Computer Sci. 20 (2018), no. 1, #18. https://doi.org/10.23638/DMTCS-20-1-18 [12] N. Kamatchi, Distance magic and distance antimagic labelings of graphs, Ph.D. thesis, Kalasalingam University, Tamil Nadu, India, 2012.
[13] G.C. Lau, H.K. Ng, and W.C. Shiu, Affirmative solutions on local antimagic chromatic numbers, Graphs Combin. 36 (2020), no. 5, 1337–1354. https://doi.org/10.1007/s00373-020-02197-2
[14] G.C. Lau, W.C. Shiu, and H.K. Ng, On local antimagic chromatic number of cycle-related join graphs, Discuss. Math. Graph Theory 4 (2021), no. 1, 133–152. http://doi.org/10.7151/dmgt.2177
[15] R. Pawar, T. Singh, A.K. Handa, and A. Godinho, Local antimagic coloring of some graphs, South East Asian J. Math. Math. Sci. 20 (2024), no. 2, 1–14. https://doi.org/10.56827/SEAJMMS.2024.2002.1
[16] V. Priyadharshini and M. Nalliah, Local distance antimagic chromatic number for the union of complete bipartite graphs, Tamkang J. Math. 54 (2023), no. 4, 281–291. https://doi.org/10.5556/j.tkjm.54.2023.4804
[17] V. Priyadharshini and M. Nalliah, Local distance antimagic chromatic number for the union of star and double graphs, Ukrainian Math. J. 75 (2023), no. 5, 765–781. https://doi.org/10.1007/s11253-023-02227-1
[18] V. Priyadharshini, A. Perrichiappan, M. Nalliah, and G.C. Lau, On local distance antimagic chromatic number of graphs disjoint union with 1-regular graphs, Proyecciones J. Math. 43 (2024), no. 2, 473–494. https://doi.org/10.22199/issn.0717-6279-5963
[19] W.C. Shiu, G.C. Lau, and M. Nalliah, Local distance antimagic chromatic number of join product of graphs with cycle or paths, Hacet. J. Math. Stat. 53 (2024), no. 3, 788–802. https://doi.org/10.15672/hujms.1266085 | ||
|
آمار تعداد مشاهده مقاله: 99 تعداد دریافت فایل اصل مقاله: 171 |
||