If A is a square-free subset of an abelian group G, then the addition graph of A on G is the graph with vertex set G and distinct vertices x and y forming an edge if and only if x+y is in A. We prove that every connected cubic addition graph on an abelian group G whose order is divisible by 8 is Hamiltonian as well as every connected bipartite cubic addition graph on an abelian group G whose order is divisible by 4. We show that connected bipartite addition graphs are Cayley graphs and prove that every connected cubic Cayley graph on a group of dihedral type whose order is divisible by 4 is Hamiltonian.
Yury J. Ionin - Central Michigan University, Mt. Pleasant, MIyury.email@example.com
Cheyne, Brian; Gupta, Vishal; and Wheeler, Coral
"Hamilton Cycles in Addition Graphs,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 4
, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol4/iss1/6