A245314 - OEIS

%I #14 Mar 28 2019 08:44:51

%S 0,3,5,8,10,13,16,19,20,22,25,28,30,32,35,38,39,42,44,47,49,52,54,57,

%T 59,60,64,66,68,71,73,76,78,81,83,85,88,91,93,95,97,100,103,105,107,

%U 110,112,115,116,119,122,124,126,129,131,134,136,139,141,143,145

%N Maximum frustration of complete bipartite graph K(n,7).

%C The maximum frustration of a graph is the maximum cardinality of a set of edges that contains at most half the edges of any cut-set.  Another term that is used is "line index of imbalance".  It is also equal to the covering radius of the coset code of the graph.

%H Robert Israel, <a href="/A245314/b245314.txt">Table of n, a(n) for n = 1..10000</a>

%H G. S. Bowlin, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i4p10/pdf">Maximum Frustration in Bipartite Signed Graphs</a>, Electr. J. Comb. 19(4) (2012) #P10.

%H R. L. Graham and N. J. A. Sloane, <a href="http://www.math.ucsd.edu/~ronspubs/85_01_covering_radius.pdf">On the Covering Radius of Codes</a>, IEEE Trans. Inform. Theory, IT-31(1985), 263-290

%H P. Solé and T. Zaslavsky, <a href="http://epubs.siam.org/doi/abs/10.1137/S0895480189174374">A Coding Approach to Signed Graphs</a>, SIAM J. Discr. Math 7 (1994), 544-553

%F a(n) = floor(154/64*n) - 1 if n = 2, 14, 17, 18, 36 or 49.

%F a(n) = floor(154/64*n) - 2 if n = 1, 3, 5, 10 or 26.

%F Otherwise a(n) = floor(154/64*n) if n == 7,12,14,16,17,22,24,26, or 27 mod 32

%F or 3,8,18,34,36,38,43,51, or 63 mod 64

%F Otherwise a(n) = floor(154/64*n) - 1.

%F a(n+64) = a(n) + 154 except for n = 1,2,3,5,10,14,17,18,26,36,49.

%F a(n) = A245230(max(n,7),min(n,7)).

%e For n=2 a set of edges that achieves the maximum cardinality a(2) = 3 is {(1,3),(1,4),(1,5)}.

%p A245314:= n -> floor(154/64*n) - piecewise(

%p           member(n,{2,14,17,18,36,49}),1,

%p           member(n,{1,3,5,10,26}),2,

%p           member(n mod 32, {7,12,14,16,17,22,24,26,27}), 0,

%p           member(n mod 64, {3,8,18,34,36,38,43,51,63}),0,

%p           1);

%p seq(A245314(n), n=1..30);

%t a[n_] := Floor[154n/64] - Which[MemberQ[{2, 14, 17, 18, 36, 49}, n], 1, MemberQ[{1, 3, 5, 10, 26}, n], 2, MemberQ[{7, 12, 14, 16, 17, 22, 24, 26, 27}, Mod[n, 32]] || MemberQ[{3, 8, 18, 34, 36, 38, 43, 51, 63}, Mod[n, 64]], 0, True, 1];

%t Array[a, 100] (* _Jean-François Alcover_, Mar 28 2019, from Maple *)

%Y Cf. A245230, A245231, A245227, A245239.

%K nonn

%O 1,2

%A _Robert Israel_, Jul 17 2014