##### International Journal of Mathematical Sciences and Computing (IJMSC)

IJMSC Vol. 7, No. 1, Feb. 2021

#### MECS Press Journal

REGULAR PAPERS

##### Labeling a kind of Cubic Graphs by Subgraph Embedding Method

DOI: https://doi.org/10.5815/ijmsc.2021.01.01, Pub. Date: 8 Feb. 2020

Based on a problem raised by Gao et. al. (Bull. Malays. Math. Sci. Soc., 41 (2018) 443–453.), we construct  a family of cubic graphs which are double-edge blow-up of ladder graphs. We determine the full friendly index sets of these cubic graphs by embedding labeling graph method. At the same time, the corresponding labeling graphs are  provided.

##### Concepts of Bezier Polynomials and its Application in Odd Higher Order Non-linear Boundary Value Problems by Galerkin WRM

DOI: https://doi.org/10.5815/ijmsc.2021.01.02, Pub. Date: 8 Feb. 2021

Many different methods are applied and used in an attempt to solve higher order nonlinear boundary value problems (BVPs). Galerkin weighted residual method (GWRM) are widely used to solve BVPs. The main aim of this paper is to find the approximate solutions of fifth, seventh and ninth order nonlinear boundary value problems using GWRM. A trial function namely, Bezier Polynomials is assumed which is made to satisfy the given essential boundary conditions. Investigate the effectiveness of the current method; some numerical examples were considered. The results are depicted both graphically and numerically. The numerical solutions are in good agreement with the exact result and get a higher accuracy in the solutions. The present method is quit efficient and yields better results when compared with the existing methods. All problems are performed using the software MATLAB R2017a.

##### A Robotic Path Planning by Using Crow Swarm Optimization Algorithm

DOI: https://doi.org/10.5815/ijmsc.2021.01.03, Pub. Date: 8 Feb. 2020

One of the most common problem in the design of robotic technology is the path planning. The challenge is choosing the robotics’ path from source to destination with minimum cost. Meta-heuristic algorithms are popular tools used in a search process to get optimal solution. In this paper, we used Crow Swarm Optimization (CSO) to overcome the problem of choosing the optimal path without collision. The results of CSO compared with two meta-heuristic algorithms: PSO and ACO in addition to a hybrid method between these algorithms. The comparison process illustrates that the CSO better than PSO and ACO in path planning, but compared to hybrid method CSO was better whenever the smallest population. Consequently, the importance of research lies in finding a new method to use a new meta-humanistic algorithm to solve the problem of robotic path planning.