Investigation of the Main Energies of Picture Fuzzy Graph and its Applications

Abstract

Abstract Picture fuzzy graph, belonging to fuzzy graphs family, has good capabilities at times when we are faced with problems that cannot be expressed by fuzzy graphs and intuitionistic fuzzy graphs. When an element membership is not clear, neutrality is a good option that can be well-supported by a picture fuzzy graph. The previous definitions limitations in fuzzy graph energy have led us to offer new definitions in picture fuzzy graphs. In this article, we expanded the energy concept on the picture fuzzy graph and sought to use this concept in modeling issues related to this graph and solving some problems including the neutrality state. We were able to show that neutrality, as part of total energy, is effective in energy-based decisions. This is noticeable in some types of energy and is more pronounced. We were looking for a way to rank the available options using the picture fuzzy graph and its Laplacian energy/energy in decision making. We studied some types of energy including Laplacian and skew Laplacian in both picture fuzzy graphs and picture fuzzy digraphs, and discussed some of its properties. We discussed some energy boundaries in this graph, and finally, the applications of energy were presented.

Keywords

• Picture fuzzy graph
• Laplacian energy
• Picture fuzzy digraph
• Skew Laplacian energy