OFFSET
1,1
COMMENTS
A positive integer k is called a magic constant if there is a simple graph G whose vertices are labeled using the numbers 1, 2, ..., |V(G)| in bijective fashion such that for each vertex v, Sum_{u in N(v)} f(u) is constant. For the first term of this sequence we use the graph P_3, a path on three vertices. Label the middle vertex 3 and other two vertices as 1 and 2 in any manner. In this setup the sums defined earlier are 3 for each vertex.
All positive integers except 1, 2, 4, 6, 8, 12, and 16 are magic constants.
LINKS
Ravindra Pawar, Tarkeshwar Singh, Himadri Mukherjee, and Jay Bagga, A Complete Characterization of all Magic Constants Arising from Distance Magic Graphs, arXiv:2311.10330 [math.CO], 2023.
CROSSREFS
KEYWORD
nonn
AUTHOR
Ravindra Pawar, Nov 21 2023
STATUS
approved