# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a245227 Showing 1-1 of 1 %I A245227 #29 Mar 27 2019 18:39:31 %S A245227 0,2,3,5,7,9,10,12,13,15,17,18,19,21,22,25,26,27,29,30,32,34,35,37,38, %T A245227 40,42,43,44,46,47,50,51,52,54,55,57,59,60,62,63,65,67,68,69,71,72,75, %U A245227 76,77,79,80,82,84,85,87,88,90,92,93,94,96,97,100,101,102 %N A245227 Maximum frustration of complete bipartite graph K(n,5). %C A245227 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 A245227 Robert Israel, Table of n, a(n) for n = 1..10000 %H A245227 G. S. Bowlin, Maximum Frustration in Bipartite Signed Graphs, Electr. J. Comb. 19(4) (2012) #P10. %H A245227 R. L. Graham and N. J. A. Sloane, On the Covering Radius of Codes, IEEE Trans. Inform. Theory, IT-31(1985), 263-290. %H A245227 P. Solé and T. Zaslavsky, A Coding Approach to Signed Graphs, SIAM J. Discr. Math 7 (1994), 544-553. %F A245227 a(n) = floor(25/16*n) - 1 if n == 2,4,9,13, or 15 mod 16 or if n = 1 or 3; a(n) = floor(25/16*n) otherwise. %F A245227 G.f.: -x^2*(x^18-x^17+x^16-x^15-3*x^14-x^13-2*x^12-x^11-x^10-2*x^9-2*x^8-x^7-2*x^6-x^5-2*x^4-2*x^3-2*x^2-x-2)/(x^17-x^16-x+1). %F A245227 a(n+16) = a(n) + 25 for n > 3. %F A245227 a(n) = A245230(max(n,5),min(n,5)). %e A245227 For n=2 a set of edges that attains the maximum cardinality a(2)=2 is {(1,3),(1,4)}. %p A245227 A245227:= n -> floor(25/16*n) - piecewise(member(n mod 16, {2,4,9,13,15}),1,0): %p A245227 A245227(1):= 0: %p A245227 A245227(3):= 3: %p A245227 seq(A245227(n),n=1..100); %t A245227 a[n_] := Floor[25 n/16] - If[n == 1 || n == 3 || MemberQ[{2, 4, 9, 13, 15}, Mod[n, 16]], 1, 0]; %t A245227 Array[a, 100] (* _Jean-François Alcover_, Mar 27 2019, after _Robert Israel_ *) %Y A245227 Cf. A245230, A245231, A245239, A245314. %K A245227 nonn %O A245227 1,2 %A A245227 _Robert Israel_, Jul 14 2014 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE