ABSTRACT
The concept of medium domination number of a graph was introduced by Duygu Vargor and Pinar Dundar. Motivated by the above, G. Mahadevan et al. introduced the concept of extended medium domination number of a graph and obtained many results. Due to many applications, again the authors introduced another concept called double twin domination number of a graph. DTwin (u, v) is the sum of number of u-v paths of length ≤4. The total number of vertices dominate every pair of vertices SDTwin(G) = ∑DTwin(u,v) for u, v ∈ V(G). The double twin domination number of G is defined as DTD ( G ) = SDTwin ( G ) ( n 2 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003038399/adc72c38-c4c0-4c8a-95bb-dbd83ca36bd4/content/C005_equ_0016.tif"/> . This concept plays a vital role in medical field. In this field, certain things should be transported to certain places (such as operation theater, accident spot, emergency unit). It is important to find how much potential number of ways are there to perform a particular task? Depending upon the task, we fix the maximum distance between one place and another places. It may be the transportation of emergency medicine to the surgery places, transportation of ambulance services to the accident spot, etc. For simplicity, we assume that the maximum distance from one node to another node is 4. This mathematical model is nothing, but finding the double twin domination number of a graph theoretical representation of the real-life situation. In this chapter, we provide a mathematical model to obtain the potential number of ways to perform certain tasks in the medical field. We obtain this number for many special types of graphs.
