A new class of disconnected antimagic graphs

Year 2024, Early Access, 1 - 14

Vinothkumar Latchoumanane Murugan V Andrea Fenovcıkova

https://doi.org/10.15672/hujms.1308520

Abstract

A graph G is antimagic if there exists a bijection f from E(G) to {1, 2, . . . , |E(G)|} such that the vertex sums for all vertices of G are distinct, where the vertex sum is defined as the sum of the labels of all incident edges. Hartsfield and Ringel conjectured that every connected graph other than K_2 admits an antimagic labeling. It is still a challenging problem to address antimagicness in the case of disconnected graphs. In this paper, we study antimagicness for the disconnected graph that is constructed as the direct product of a star and a path.

Keywords

direct product, disconnected graph, antimagic labeling, star, path

Supporting Institution

Slovak Research and Development Agency

Project Number

APVV-19-0153 and VEGA 1/0243/23

Thanks

Slovak Research and Development Agency

References

• [1] N. Alon, G. Kaplan, A. Lev, Y. Roditty and R. Yuster, Dense graphs are antimagic, J. Graph Theory 47 (4), 297–309, 2004.