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A348600
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Triangle read by rows: T(n,k) is the number of (unlabeled) connected graphs with n nodes and metric dimension k, 0 <= k < n.
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0
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1, 0, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 13, 6, 1, 0, 1, 62, 39, 9, 1, 0, 1, 275, 488, 77, 11, 1, 0, 1, 1710, 8116, 1145, 130, 14, 1, 0, 1, 12061, 216432, 29958, 2415, 196, 16, 1, 0, 1, 93706, 9512947, 2026922, 78265, 4434, 276, 19, 1
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OFFSET
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1,9
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LINKS
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FORMULA
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T(n,1) = 1 for n >= 2, because the only graphs with metric dimension 1 are the paths of positive lengths (Chartrand et al. 2000).
T(n,n-2) = A047209(n-2) = floor(5*n/2-6) for n >= 3 (follows from the complete description of graphs with n nodes and metric dimension n-2 by Chartrand et al. 2000).
T(n,n-1) = 1 for n >= 1 , because the only graph with n nodes and metric dimension n-1 is the complete graph (Chartrand et al. 2000).
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EXAMPLE
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Triangle begins:
n\k| 0 1 2 3 4 5 6 7 8 9
---+------------------------------------------------
1 | 1
2 | 0 1
3 | 0 1 1
4 | 0 1 4 1
5 | 0 1 13 6 1
6 | 0 1 62 39 9 1
7 | 0 1 275 488 77 11 1
8 | 0 1 1710 8116 1145 130 14 1
9 | 0 1 12061 216432 29958 2415 196 16 1
10 | 0 1 93706 9512947 2026922 78265 4434 276 19 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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