A367539 Sequence of magic constants related to distance magic graphs.

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

Table of n, a(n) for n=1..68.

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

Adjacent sequences: A367536 A367537 A367538 * A367540 A367541 A367542

Keyword

nonn

Author

Ravindra Pawar, Nov 21 2023

Status

approved