1 research outputs found
Edge-magic labelings for constellations and armies of caterpillars
Let be an -vertex graph with edges. A function is an edge-magic labeling of if is
bijective and, for some integer , we have for every
edge . Furthermore, if , then we say that
is a super edge-magic labeling. A constellation, which is a collection of
stars, is symmetric if the number of stars of each size is even except for at
most one size. We prove that every symmetric constellation with an odd number
of stars admits a super edge-magic labeling. We say that a caterpillar is of
type if and are the sizes of its parts, where . We
also prove that every collection with an odd number of same-type caterpillars
admits an edge-magic labeling