in this paper, some results of singh, gopalakrishna and kulkarni (1970s) have been extended to higher order derivatives. it has been shown that, if $sumlimits_{a}theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $t(r, f)sim t(r, f^{(k)}), rrightarrowinfty$ if $theta(infty, f)=1$ and $t(r, f)sim (k+1)t(r, f^{(k)}), rrightarrowinfty$ if $th...

In this paper, some results of Singh, Gopalakrishna and Kulkarni (1970s) have been extended to higher order derivatives. It has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), rrightarrowinfty$ if $Th...

The bandwidth of a graph is the minimum, over vertex labelings using distinct integers, of the maximum diierence between labels of adjacent ver-tices. Let f(n) denote the maximum sum of the bandwidths of complementary n-vertex graphs. Chinn, Chung, Erd} os, and Graham 3] proved the existence of constants c 1 ; c 2 such that 2n ? c 2 log n f(n) 2n ? c 1 log n. We sharpen this to 2n ? 8 log 2 n ?...

Abstract Huemer et al. (Discrete Mathematics, 2019) proved that for any two point sets R and B with $$|R|=|B|$$ | R = B , the perfect matching matches points of maximizes total squared Euclidean distance matched pairs, has property all ...