scholarly journals A Novel Mathematical Model for Radio Mean Square Labeling Problem

2022 ◽  
Vol 2022 ◽  
pp. 1-9
Author(s):  
Elsayed Badr ◽  
Shokry Nada ◽  
Mohammed M. Ali Al-Shamiri ◽  
Atef Abdel-Hay ◽  
Ashraf ELrokh

A radio mean square labeling of a connected graph is motivated by the channel assignment problem for radio transmitters to avoid interference of signals sent by transmitters. It is an injective map h from the set of vertices of the graph G to the set of positive integers N , such that for any two distinct vertices x , y , the inequality d x , y +   h x 2 + h y 2 / 2   ≥ dim G + 1 holds. For a particular radio mean square labeling h , the maximum number of h v taken over all vertices of G is called its spam, denoted by rmsn h , and the minimum value of rmsn h taking over all radio mean square labeling h of G is called the radio mean square number of G , denoted by rmsn G . In this study, we investigate the radio mean square numbers rmsn P n and rmsn C n for path and cycle, respectively. Then, we present an approximate algorithm to determine rmsn G for graph G . Finally, a new mathematical model to find the upper bound of rmsn G for graph G is introduced. A comparison between the proposed approximate algorithm and the proposed mathematical model is given. We also show that the computational results and their analysis prove that the proposed approximate algorithm overcomes the integer linear programming model (ILPM) according to the radio mean square number. On the other hand, the proposed ILPM outperforms the proposed approximate algorithm according to the running time.

2012 ◽  
Vol 548 ◽  
pp. 767-771 ◽  
Author(s):  
C. Vanlisuta ◽  
Suksan Prombanpong

The objective of this paper is to determine the number and species of trees to be planted in order to maximize a profit through an integer linear programming model. The mathematical model is developed in terms of the profit function. This objective function is therefore, a difference between carbon credit revenue and costs of plantation. The economical plants are only considered in the model. Consequently, fourteen different tree species are to be investigated. The objective function is subjected to several constraints i.e. planting area, carbon sequestration and so on. The planting envelope of each tree is assigned 4 by 4 meters. In this paper, the Eastern part of Thailand is considered the case study. It is found that three kinds of plants, Copper pod, Cananga, and Bullet wood are suitable for planting. A number of trees to be planted in 1600 square meter are twenty, thirty, and fifty plants respectively. The profit earned is of 12,112 $ per year in the next fifth year.


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