Some Aspects on Fully Complete Domination in Picture Fuzzy Graphs Based on Strong Edges - Rajathi, N.; Anusuya, V.; Gani, A. Nagoor (Communications in Mathematics and Applications, 2022)
Picture fuzzy graph is an efficient mathematical tool for dealing ambiguous real world problems where the fuzzy graph and intuitionistic fuzzy graph would not produce high accuracy. It can be very useful in situations in which there are multiple choices of such type: yes, no, abstain and refusal. The primary aim of this study is to define the fully complete domination in picture fuzzy graph based on strong edges. Due to the importance of the notion of domination and its applications in various situations, The fully complete picture fuzzy dominating set is introduced. In addition, many significant properties related to this parameter are obtained. Further, the relation between the fully complete picture fuzzy domination number and picture fuzzy domination number is discussed. Some theorems are proved with suitable examples. An algorithm is provided to compute the fully complete picture fuzzy dominating set and its domination number and verified through an example.
Keywords: Picture fuzzy graph; Fully complete picture fuzzy dominating set; Fully complete picture fuzzy domination number; Strong edge; Strong neighbors