Total dominator chromatic number of graphs with specific construction
ODAM-Vol. 3 (2020), Issue 2, pp. 1 – 7 Open Access Full-Text PDF
Saeid Alikhani, Nima Ghanbari
Abstract: Let \(G\) be a simple graph. A total dominator coloring of \(G\) is a proper coloring of the vertices of \(G\) in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number \(\chi_d^t(G)\) of \(G\) is the minimum number of colors among all total dominator coloring of \(G\). In this paper, we study the total dominator chromatic number of some graphs with specific construction. Also we compare \(\chi_d^t(G)\) with \(\chi_d^t(G-e)\), where \(e\in E(G)\).
A modified efficient difference-type estimator for population mean under two-phase sampling design
OMS-Vol. 4 (2020), Issue 1, pp. 195 – 199 Open Access Full-Text PDF
A. E. Anieting, J. K. Mosugu
Abstract: In this article, modified difference-type estimator for the population mean in two-phase sampling scheme using two auxiliary variables has been proposed. The mean squared error of the proposed estimator has also been derived using large sample approximation. The efficiency comparison conditions for the proposed estimator in comparison with other existing estimators in which the proposed estimator performed better than the other relevant existing estimators have been given.
Generalized the Liouville’s and Möbius functions of graph
OMS-Vol. 4 (2020), Issue 1, pp. 186 – 194 Open Access Full-Text PDF
Hariwan Fadhil M. Salih, Shadya Merkhan Mershkhan
Abstract: Let \(G = (V,E)\) be a simple connected undirected graph. In this paper, we define generalized the Liouville’s and Möbius functions of a graph \(G\) which are the sum of Liouville \(\lambda\) and Möbius \(\mu\) functions of the degree of the vertices of a graph denoted by \(\Lambda(G)=\sum\limits_{v\in V(G)}\lambda(deg(v))\) and \(M(G)=\sum\limits_{v\in V(G)}\mu(deg(v))\), respectively. We also determine the Liouville’s and Möbius functions of some standard graphs as well as determining the relationships between the two functions with their proofs. The sum of generalized the Liouville and Möbius functions extending over the divisor d of degree of vertices of graphs is also given.
Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials
OMS-Vol. 4 (2020), Issue 1, pp. 179 – 185 Open Access Full-Text PDF
Nabiha Saba, Ali Boussayoud
Abstract: In this paper, we introduce a symmetric function in order to derive a new generating functions of bivariate Pell Lucas polynomials. We define complete homogeneous symmetric functions and give generating functions for Gauss Fibonacci polynomials, Gauss Lucas polynomials, bivariate Fibonacci polynomials, bivariate Lucas polynomials, bivariate
Jacobsthal polynomials and bivariate Jacobsthal Lucas polynomials.
Jacobsthal polynomials and bivariate Jacobsthal Lucas polynomials.
Second mixed problem for an Euler-Poisson-Darboux equation with dirac potential
OMS-Vol. 4 (2020), Issue 1, pp. 174 – 178 Open Access Full-Text PDF
Kaman Mondobozi Lélén, Togneme Alowou-Egnim, Gbenouga N’gniamessan, Tcharie Kokou
Abstract: We establish the strong generalized solution of the second mixed problem for an Euler-Poisson-Darboux equation in which the free term has the form: \(\gamma(t) u(x_0,t_0)\) where \(u(x,t)\) is the unknown function sought at the point \((x_0,t_0).\)
Covering radius of repetition codes over \(F_{2}+vF_{2}+v^2F_2\) with \(v^3=1\)
OMS-Vol. 4 (2020), Issue 1, pp. 168 – 173 Open Access Full-Text PDF
Sarra Manseri, Jinquan Luo
Abstract: In this paper, the exact value of covering radius of unit repetition codes and the bounds of covering radius of zero-divisor repetition codes have been determined by using Lee weight over the finite ring \(F_{2}+vF_{2}+v^2F_2\). Moreover the covering radius of different block repetition codes have been also studied.
