Abstract
An edge labeling of graph G with labels in A is an injection from E G to A , where E G is the edge set of G , and A is a subset of ℝ . A graph G is called ℝ -antimagic if for each subset A of ℝ with A = E G , there is an edge labeling with labels in A such that the sums of the labels assigned to edges incident to distinct vertices are different. The main result of this paper is that the Cartesian products of complete graphs (except K 1 ) and cycles are ℝ -antimagic.
Highlights
A graph G is antimagic if G is {1, 2, . . . , |E(G)|}-antimagic. e concept of antimagic graphs was introduced by Hartsfield and Ringel [1] in 1990
In 2008, Wang and Hsiao [6] introduced new classes of antimagic graphs constructed through Cartesian products, and Wang [7] proved that any Cartesian product of two or more cycles is antimagic. e antimagicness of the Cartesian products of two paths and the Cartesian products of two or more regular graphs are proved in [8, 9] by Cheng
EGn−1(wm,n−1) and A2 wm,n−1wm,n. en, Corollary 2. e graph G1□G2□ · · · □Gn (n ≥ 2) is uniformly R-antimagic, where each Gi is a complete graph of order ≥2 or a cycle
Summary
A graph G is antimagic if G is {1, 2, . . . , |E(G)|}-antimagic. e concept of antimagic graphs was introduced by Hartsfield and Ringel [1] in 1990. Ey conjectured that every connected graph with at least two edges was antimagic. En, Chang et al [5] proved that all regular graphs with degree ≥2 are antimagic. E antimagicness of the Cartesian products of two paths and the Cartesian products of two or more regular graphs are proved in [8, 9] by Cheng. Matamala and Zamora [11] proved that paths, cycles, and graphs whose connected components are cycles or paths of odd lengths are universal antimagic in 2020.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
