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A367539
Sequence of magic constants related to distance magic graphs.
0
3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75
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
Sequence in context: A344000 A128938 A215138 * A093373 A096849 A369361
KEYWORD
nonn
AUTHOR
Ravindra Pawar, Nov 21 2023
STATUS
approved