Characterization of completely k-magic regular graphs

• Main Authors: Eniego, Arnold A, Garces, Ian June L
• Format: text
• Published: Archīum Ateneo 2016
• Subjects: Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/54; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1053&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

Let k ∈ N and c ∈ Zk. A graph G is said to be c-sum k-magic if there is a labeling ` : E(G) → Zk \ {0} such that P u∈N(v) `(uv) ≡ c (mod k) for every vertex v of G, where N(v) is the neighborhood of v in G. We say that G is completely k-magic whenever it is c-sum k-magic for every c ∈ Zk. In this paper, we characterize all completely k-magic regular graphs.