Given a graph G on n vertices and two integers k d, the Contraction(vc) problem asks whether one can contract at most edges to reduce vertex cover number of by least d. Recently, Lima et al. [JCSS 2021] proved that admits an XP algorithm running in time f(d)⋅nO(d). They asked this is FPT under parameterization. In article, we prove that: (i) W[1]-hard parameterized k+d. Moreover, unless ETH fai...

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} is called local edge antimagic labeling if for any two adjacent edges e uv e’ vw G, we have w(e) ≠ w(e’), where the weight w(e uv) f(u)+f(v) w(e’) f(v)+f(w). has labeling. The chromatic number χ’lea(G) defined to minimum colors taken over all colorings induced by labelings G. In thi...

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph $G$ denoted by $chi_a '(G)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. The maximum degree in $G$ denoted by $Delta(G)$, is the lower bound for $chi_a '(G)$. $P$-cuts introduced in this paper acts as a powerfu...

In the integration of geodetic networks with different geodetic coordinate systems, the similarity transformation seems to be the most suitable method because the geodetic coordinate systems are designated to be Cartesian (orthogonal). However, this method may always not be practical to use in most surveying works demanding such high accuracies as the coordinates used in the transformation are ...