Local Face Antimagic Evaluations and Coloring of Plane Graphs

• Autorzy: Bong Novi , Bača Martin , Semaničová-Feňovčíková Andrea , Sugeng Kiki A. , Wang Tao-Ming

Identyfikatory

DOI

10.3233/FI-2020-1934

• Języki publikacji: EN

Abstrakty

EN

We investigate a local face antimagic labeling of plane graphs, and we introduce a new graph characteristic, namely local face antimagic chromatic number of type (a, b, c). Then we determine the precise value of this parameter for wheels and ladders.

Słowa kluczowe

EN

local face antimagic; chromatic number of type (a, b, c); local face antimagic labeling; plane graph

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2020
• Tom: Vol. 174, nr 2
• Strony: 103--119
• Opis fizyczny: Bibliogr. 20 poz., rys.

Twórcy

autor

Bong Novi

• Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA.

autor

Bača Martin

• Department of Applied Mathematics and Informatics, Technical University, Košice, Slovak Republic

autor

Semaničová-Feňovčíková Andrea

• Department of Applied Mathematics and Informatics, Technical University, Košice, Slovak Republic

autor

Sugeng Kiki A.

• Department of Mathematics, University of Indonesia, Kampus UI Depok, Depok 16424, Indonesia

autor

Wang Tao-Ming

• Department of Applied Mathematics, Tunghai University, Taichung, Taiwan, ROC

Bibliografia

• [1] Hartsfield N, Ringel G. Pearls in Graph Theory. Boston: Academic Press, 1994.
• [2] Cheng Y. Latice grids and prisms are antimagic. Theor. Comput. Sci., 2007. 374(1-3):66-73. doi:10.1016/j.tcs.2006.12.003.
• [3] Cheng Y. A new class of antimagic Cartesian product graphs. Discrete Math., 2008. 308(24):6441-6448. doi:10.1016/j.disc.2007.12.032.
• [4] Gallian J. A dynamic survey of graph labeling. The Electronic J. Combin., 2017. #DS6.
• [5] Wang TM. Toroidal grids are anti-magic. In: Wang L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg. 3595:671-679. doi:10.1007/11533719_68.
• [6] Cranston DW, Liang YC, Zhu X. Regular graphs of odd degree are antimagic. J. Graph Theory, 2015. 80:28-33. doi:10.1002/jgt.21836.
• [7] Bércz K, Bernáth A, Vizer M. Regular graphs are antimagic. Electron. J. Comb., 2015. 22(3). doi:10.37236/5465.
• [8] Chang F, Liang YC, Pan Z, Zhu X. Antimagic labeling of regular graphs. J. Graph Theory, 2016. 82:339-349. doi:10.1002/jgt.21905.
• [9] Bača M, Miller M. On d-antimagic labelings of type (1, 1, 1) for prisms. J. Combin. Math. Combin. Comput., 2003. 44:199-207.
• [10] Lih KW. On magic and consecutive labelings of plane graphs. Utilitas Math., 1983. 24:165-197.
• [11] Ali G, Bača M, Bashir F, Semaničová-Feňovčíková A. On face antimagic labelings of disjoint union of prisms. Utilitas Math., 2011. 85:97-112.
• [12] Bača M, Baskoro ET, Jendrol’ S, Miller M. Antimagic labelings of hexagonal planar maps. Utilitas Math., 2004. 66:231-238.
• [13] Bača M, Brankovic L, Semaničová-Feňovčíková A. Labelings of plane graphs containing Hamilton path. Acta Math. Sin. (Engl. Ser.), 2011. 27(4):701-714. doi:10.1007/s10114-011-9451-x.
• [14] Bača M, Miller M, Phanalasy O, Semaničová-Feňovčíková A. Super d-antimagic labelings of disconnected plane graphs. Acta Math. Sin. (Engl. Ser.), 2010. 26(12):2283-2294. doi:10.1007/s10114-010-9502-8.
• [15] K.A. Sugeng, M. Miller, Y. Lin and M. Bača Face antimagic labelings of prisms. Utilitas Math., 2006. 71:269-286.
• [16] Arumugam S, Premalatha K, Bača M, Semaničová-Feňovčíková A. Local antimagic vertex coloring of a graph. Graphs Combin, 2017. 33:275-285. doi:10.1007/s00373-017-1758-7.
• [17] Bensmail J, Senhaji M, Szabo Lyngsie K. On a combination of the 1-2-3 conjecture and the antimagic labelling conjecture. Discrete Math. Theoret. Comput. Sci., 2017. 19. arXiv:1704.01172.
• [18] Haslegrave J. Proof of a local antimagic conjecture. Discrete Math. Theoret. Comput. Sci., 2018. 20(1):#18. doi:10.23638/DMTCS-20-1-18.
• [19] Bača M, Miller M, Phanalasy O, Ryan J, Semaničová-Feňovčíková A, Sillasen AA. Every plane graph is antimagic. preprint.
• [20] West DB. Introduction to Graph Theory. (2nd Edition). Prentice - Hall, 2000. ISBN-13: 978-0130144003, 10: 0130144002.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).