Anti-magic labeling on a class of sparse graphs - Tai, Yu Bin (2023)
In 1990, Hartsfield and Ringel first introduced the anti-magic labeling and conjectured that every graph other than the complete graph with 2 vertices has an anti-magic labeling. This conjecture has been verified for regular graphs and some classes of trees. In this dissertation we shall prove the anti-magicness of a class of sparse graphs. The thesis begins with a survey on some graph labelings, including antimagic labeling. The thesis continues by introducing graph decompositions and some applications of graph labelings. In the next chapter, we proved that multibridge graphs are anti-magic. The thesis is concluded with a discussion on the anti-magicness of families of sparse graphs obtained by overlapping the multi-bridge graph with itself or with some extended friendship graph. The proof of the anti-magicness of these families of sparse graphs is left as an open problem for future research.