A Study on Connected Domination Transition Number of a Graph - S, Kaspar; Gayathri, B.; Kalpanapriya, D.; P. Kulandaivel, M. (International Journal of Engineering and Technology, 2018)
Since its inception, the notion of domination has found vital roles in several real life applications related to facility locations, representativesâ€™ selection, communication networks, electrical networks, etc. The vast application of the notion has paved the way for the development of the notion with several types. The notion of connected domination is a significant domination parameter amongst the several domination varieties emerged in this domain. The problem of determining limited bus stops in a route was effectively addressed by the connected domination parameter. Most of the biological and neural networks effectively use this notion to solve several problems which require the connectedness of the structures. In view of the growing applications of the variant, several researchers and scholars have published numerous research articles on the said parameter. Recently, some researchers attempted on transition of the domination parameter into a connected one. In order to facilitate this transition, another variant viz., connected domination transition number was introduced and its properties and bounds were studied. In this article we explore more properties and bounds of the parameter connected domination transition number for special types of graphs. We also characterize the instances at which the domination and connected domination parameters would be same for few types of graphs. We also attempted to derive few Nordhausâ€“Gaddum (NG) type results for the same.Â