2023/10/11 by Latchoumanane, Vinothkumar, Varadhan, Murugan
#05C76 #05C78 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2310.07114
A graph G with p vertices and q edges has an antimagic labelling if there is a bijection from the graph's edge set to the label set \1,2, ⋯, q \ such that p vertices must have distinct vertex sums, where the vertex sums are determined by adding up all the edge labels incident to each vertex v in V(G). Hartsfield and Ringel \citeRingel1 in the book "Pearls in Graph Theory" conjectured that every connected graph is antimagic, with the exception of P2. In this study, we identified a class of connected graphs that lend credence to the conjecture. In this article, we proved that the tensor product of a wheel and a star, a helm and a star, and a flower and a star is antimagic.