The Cartesian product of wheel graph and path graph is antimagic

Document Type : Original paper


Christ University


Suppose each edge of a simple connected undirected graph is given a unique number from the numbers $1, 2, \dots, $q$, where $q$ is the number of edges of that graph. Then each vertex is labelled with sum of the labels of the edges incident to it. If no two vertices have the same label, then the graph is called an antimagic graph. We prove that the Cartesian product of wheel graph and path graph is antimagic.


Main Subjects

[1] S. Arumugam, M. Miller, O. Phanalasy, and J. Ryan, Antimagic labeling of generalized pyramid graphs, Acta Math. Sin. (Engl. Ser.) 30 (2014), no. 2, 283–290.
[2] M. Bača, O. Phanalasy, J. Ryan, and A. Semaničová-Feňovčíková, Antimagic labelings of join graphs, Math. Comput. Sci. 9 (2015), no. 2, 139–143.
[3] D. Buset, M. Miller, O. Phanalasy, and J. Ryan, Antimagicness for a family of generalized antiprism graphs, Electron. J. Graph Theory Appl. 2 (2014), no. 1, 42–51.
[4] Y. Cheng, Lattice grids and prisms are antimagic, Theoret. Comput. Sci. 374 (2007), no. 1-3, 66–73.
[5] J.A. Gallian, A dynamic survey of graph labeling, Electro. J. Combin. 1 (2020), no. Dynamic Surveys.
[6] N. Hartsfield and G. Ringel, Pearls in Graph Theory: A Comprehensive Introduction, San Diego, CA: Academic Press, 1990.
[7] P.C.B. Li, Antimagic labelings of power of cycles graphs, Department of Computer Science, University of Manitoba, Canada, 2011.
[8] O. Phanalasy, M. Miller, C.S. Iliopoulos, S.P. Pissis, and E. Vaezpour, Construction of antimagic labeling for the Cartesian product of regular graphs, Math. Comput. Sci. 5 (2011), no. 1, 81–87.
[9] T. Wang, M.J. Liu, and D.M. Li, A class of antimagic join graphs, Acta Math. Sin. (Engl. Ser.) 29 (2013), no. 5, 1019–1026.
[10] T.-M. Wang, Toroidal grids are anti-magic, International Computing and Combinatorics Conference, Springer, 2005, pp. 671–679.
[11] Y. Zhang and X. Sun, The antimagicness of the Cartesian product of graphs, Theoret. Comput. Sci. 410 (2009), no. 8-10, 727–735.