A graph G of order p and size q is edge-magic if there is a bijective function f : V (G) ∪ E(G) −→ {i} i=1 such that f(x) + f(xy) + f(y) = k, for all xy ∈ E(G). The function f is an edge-magic labeling of G and the sum k is called either the magic sum, the valence or the weight of f . Furthermore, if f(V (G)) = {i}pi=1 then f is a super edge-magic labeling of G. In this paper we study the valen...

In this paper we survey the behavior of various graph operations on the graph parameters clique-width and NLC-width. We give upper and lower bounds for the clique-width and NLC-width of the modi ed graphs in terms of the clique-width and NLC-width of the involved graphs. Therefor we consider the binary graph operations join, co-join, sum, di erence, products, corona, substitution, and 1-sum, an...

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...

background: liver cancer mortality is high in thailand but utility of related vital statistics is limited due to national vital registration (vr) data being under reported for specific causes of deaths. accurate methodologies and reliable supplementary data are needed to provide worthy national vital statistics. this study aimed to model liver cancer deaths based on verbal autopsy (va) study in...

Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.

0≤n<x:n≡l( mod m) (−1)g In the case q = 2 we write Sm,l,2 = Sm,l, σ2(n) = σ(n). We call (2) a generalized Newman sum. In [7] we gave a quite another proof of the Coquet’s estimates for S3,0(x) and a fast algorithm for its calculation. Professor J.-P.Allouche kindly informed me about a misprint in Coquet’s theorem: for odd x η = η(x) = (−1) (but (−1) as in [2]; sf. [1], pp.98-99) An important ro...

Let σ n be the sum of all divisors id="M2"> and let id="M3"> open="[" close="]" t integral part id="M4"> . In this paper, we shall prove that id="M5"> ∑ ≤ x</m...