The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph Ln with m-pendant Ln mk1 is odd graceful. We also show that the subdivision of ladder graph Ln with m-pendant S(Ln)  mk1 is odd grace...

Surface roughness, often captured through root-mean-square roughness (Rrms), has been shown to impact the quality of self-assembled monolayers (SAMs) formed on coinage metals. Understanding the effect of roughness on hydrophobicity of SAMs, however, is complicated by the odd-even effect-a zigzag oscillation in contact angles with changes in molecular length. We recently showed that for surfaces...

A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even-odd rule and the winding number, the former leading to ray-crossing, the latter to angle summation algorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algor...

A graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function f∗ : E(G) → {1, 3, · · · , 2q − 1} defined by f∗(uv) = f(u) + f(v) is a bijection. A graph that admits odd harmonious labeling is called odd harmonious graph. In this paper, we prove that shadow and splitting of graph K2,n, Cn for n ≡ 0 (mod 4), the grap...

In this paper, we prove that the square graph of bistar Bn,n, the splitting graph of Bn,n and the splitting graph of star K1,n are graceful graphs. We also prove that the splitting graph and the shadow graph of bistar Bn,n admit odd graceful labeling.

We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi–magic nuclei in the framework of self–consistent nuclear mean–field models. The equations for the conventional BCS model and the approximate projection–before–variation Lipkin–Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipki...

We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glaßer et al. [17] in the context of CSPs and settle the major open question from that paper, finding a certain satisfaction problem on circuits to be decidable. This we prove using the decidability of Skolem Arithmetic. We continue by studying first-order expans...