The decay number of a connected graph is defined to be the minimum number of the components of the cotree of the graph. Upper bounds of the decay numbers of gra
We prove that the inequality m+n/mn+min{m,n}≤m m∑i=1(n∑j=1xij)^2+n n∑j=1(m∑i=1xij)^2/(m∑i=1 n∑j=1xij)^2+mn m∑i=1 n∑j=1x^2ij holds, when a m×n real matri