Total and Secure Domination for Corona Product of Two Fuzzy Soft Graphs

Abstract

Fuzzy sets and soft sets are two different soft computing models for representing vagueness and uncertainty. On the other domination is a rapidly developing area of research in graph theory, and its various applications to ad hoc networks, distributed computing, social networks and web graphs partly explain the increased interest. This concept was introduced by [Benecke S, Cockayne EJ, Mynhardt CM. Secure total domination in graphs. Util Math. 2007;74:247–259.] in 2007 and Go and Canoy continue the study of these notions [Canoy RS, Go CE. Domination in the corona and join of graphs. Int Math Forum. 2011;6(16):763–771.] and afterward introduce total dominating and secure total dominating sets. Also graph operations like corona product play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In this paper, we characterised the dominating, total dominating, and secure total dominating sets in the corona of two fuzzy soft connected.