cp's OEIS Frontend

A348600 Triangle read by rows: T(n,k) is the number of (unlabeled) connected graphs with n nodes and metric dimension k, 0 <= k < n.

%I A348600 #9 Jan 27 2022 21:00:42
%S A348600 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,
%T A348600 1710,8116,1145,130,14,1,0,1,12061,216432,29958,2415,196,16,1,0,1,
%U A348600 93706,9512947,2026922,78265,4434,276,19,1
%N A348600 Triangle read by rows: T(n,k) is the number of (unlabeled) connected graphs with n nodes and metric dimension k, 0 <= k < n.
%H A348600 Gary Chartrand, Linda Eroh, Mark A. Johnson, and Ortrud R. Oellermann, <a href="https://doi.org/10.1016/S0166-218X(00)00198-0">Resolvability in graphs and the metric dimension of a graph</a>, Discrete Applied Mathematics 105 (2000), 99-113.
%H A348600 Richard C. Tillquist, Rafael M. Frongillo, and Manuel E. Lladser, <a href="https://arxiv.org/abs/2104.07201">Getting the lay of the land in discrete space: a survey of metric dimension and its applications</a>, arXiv:2104.07201 [math.CO], 2021.
%H A348600 Wikipedia, <a href="https://en.wikipedia.org/wiki/Metric_dimension_(graph_theory)">Metric dimension</a>
%F A348600 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).
%F A348600 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).
%F A348600 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).
%e A348600 Triangle begins:
%e A348600   n\k| 0  1     2       3       4     5    6   7  8  9
%e A348600   ---+------------------------------------------------
%e A348600    1 | 1
%e A348600    2 | 0  1
%e A348600    3 | 0  1     1
%e A348600    4 | 0  1     4       1
%e A348600    5 | 0  1    13       6       1
%e A348600    6 | 0  1    62      39       9     1
%e A348600    7 | 0  1   275     488      77    11    1
%e A348600    8 | 0  1  1710    8116    1145   130   14   1
%e A348600    9 | 0  1 12061  216432   29958  2415  196  16  1
%e A348600   10 | 0  1 93706 9512947 2026922 78265 4434 276 19  1
%Y A348600 Cf. A047209, A303735.
%Y A348600 Row sums: A001349.
%K A348600 nonn,tabl
%O A348600 1,9
%A A348600 _Pontus von Brömssen_, Jan 26 2022