#I implemented Corollary 1.3 of \cite{CioabaGu2016}, where an upper bound of $d-1+\frac{2}{d}$
#is shown to be sufficient to guarantee 2-connectivity for simple graphs

#We scan d-regular GRAPHS of size n and implement Sebis&Gu bound (Corollary 1.3)####################################################################
n=4
L=list(graphs(n))
print "Total number of graphs:",len(L)
for i in range(len(L)):
        if L[i].is_regular() and L[i].is_connected():
                d=L[i].degree(0)
                A=L[i].adjacency_matrix()
                spectrum=A.eigenvalues()
                orderedspectrum=sorted(spectrum)
                lambda2=orderedspectrum[n-2]
                if d%2==0 and lambda2<(d-2+sqrt(d^2+12))/2:
                    SebiGubound=(d-2+sqrt(d^2+12))/2
                    print "SebiGu upper bound on lambda2:", numerical_approx(SebiGubound)
                    print "even degree:", d
                    print "spectrum A:", orderedspectrum
                    print "lambda2:", lambda2
                    show(L[i])
                else:
                    if lambda2<(d-2+sqrt(d^2+8))/2:
                        SebiGubound=(d-2+sqrt(d^2+8))/2
                        print "SebiGu upper bound on lambda2:", numerical_approx(SebiGubound)
                        print "odd degree:", d
                        print "spectrum A:", orderedspectrum
                        print "lambda2:", lambda2
                        show(L[i])