For every \(n\ge 3\), we determine the minimum number of edges of graph with \(n\) vertices such that for any non edge \(xy\) there exits a hamiltonian cycle containing \(xy\).

In this paper we characterize a bounded vector measure on Lie compact group \(G = GL(2;\mathbb{R})\). It is a question of considering a bounded vector measure \(m\) defined from \(K(G;E)\) the space of \(E\) valued functions with compact support on \(G\) and giving its integral form.

In this research work, we applied some solving techniques on Travelling salesman problem (TSP) and Capaciated Vehicle routing problem (CVRP) which are some of the variants of vehicle routing problem. For each of the considered problem, Branch-and-cut was applied on TSP and Column generation technique was used on CVRP. We obtained optimal solution and tour. Hence, these methods can be used to solve similar problem for optimal solution.

In this paper, we investigate the equivalence between the Backlund transformation of Riccati equation method and the extended tanh-function method. It is proved that the two methods are equivalent when applying them to partial differential equations and differential-difference equations. Two examples are introduced to justify our results.

In this paper, we will determine the 3-total edge product cordial (3-TEPC) labeling. We study certain classes of graphs namely tadpole, book and flower graphs in the context of 3-TEPC labeling.

In this paper, the notion of some algebraic properties of fundamental group of intuitionistic fuzzy topological spaces (IFTSs) are introduced. We give a necessary and sufficient condition for a fundamental group of IFTSs to be abelian, a necessary and sufficient conditions for a subset of fundamental group of IFTSs to be subgroup, a necessary and sufficient condition for a subgroup of fundamental group of IFTSs to be normal and a necessary and sufficient condition for an element to be in a center of fundamental group of IFTSs. We also describe the set of centralizers of an element in a fundamental group of IFTSs and the quotient fundamental group of IFTSs.

In this paper, a coupled fixed point theorem for maps satisfying rational type contractive condition in the perspective of dislocated quasi b-metric space have been formed and the existence and uniqueness of a couple fixed point have been proved. Our result improves and generalizes comparable results in the literature.

This research focuses on the effect salinity on the structural strengths of conventional concrete. The unreinforced beam, cylinder and cube specimens produced were cured up to 120 days in different curing medium and tested at varying predetermined curing age. The physio-chemical properties of Unilag tap and lagoon water, physical properties, workability, compressive, split tensile and flexural strengths were determined. Two curing media (salt water I & salt water II) having five times (5\(\times\)) and ten times (10\(\times\)) the chloride content of lagoon water were simulated. The results revealed that the structural strengths of concrete samples cured in lagoon water recorded lower strengths when compared to samples cured in salt water I but higher in strength development than samples cured in salt water II. The percentage decrease in structural strengths increased from lagoon water to salt water II which recorded the highest value of 29.35%, 17.67% and 33.65% at 28-day for compressive, tensile and flexural strengths respectively. The mathematical models developed using Modified Regression Approach to predict the structural strengths were in good agreement with the experimental data. This research reveals that the salt water solution simulation in the laboratory does not fully replicate the aggressiveness of actual marine water (environment).

This article maintains that the impossibility of trisection is based on a cubic polynomial whose trigonometric content is not clear; or, the impossibility may be referring to one particular trisection method even if the cubic equation does constitute the equation of trisection. It next proceeds to trisection “indirectly” by attempting to construct one of the two trisectors on the basis of reductio ad absurdum.

In this paper, the approach to obtaining nontrivial formulas for some recursively defined sequences is illustrated. The most interesting result in the paper is the formula for the solution of quadratic map-like recurrence. Also, some formulas for the solutions of linear difference equations with variable coefficients are obtained. At the end of the paper, some integer sequences associated with a quadratic map are considered.