On the Barycentric Labeling of Certain Graphs. (16th November 2014) - Alikhani, Saeid; Amirzadeh, Zeynab
Abstract : LetA be an abelian group. A graphG is calledA -magic if there exists edge labelingl : E ( G ) → A ∖ 0 such that the induced vertex set labelingl + : V ( G ) → A, defined byl + ( v ) = ∑ u v ∈ E ( G ) ‍ l ( u v ), where the sum is over all edges inE ( G ), is a constant map. A graphG isA -barycentric-magic (or hasA -barycentric labeling) ifG isA -magic and also satisfiesl + ( v ) = deg ( v ) l ( u v v ) for allv ∈ V and for some vertexu v adjacent tov . In this paper we consider some graphsG and characterize allm ∈ N for whichG isZ m -barycentric-magic.