A study on m-polar fuzzy detour g-boundary node and m-polar fuzzy detour g-interior node of an m-polar fuzzy and application

In this article, we introduce the concepts of m-polar fuzzy (mPF) detour gboundary nodes and mPF detour g-interior nodes within m-polar fuzzy graphs (mPFGs). We explore their significance and examine their properties. Furthermore, we establish a relationship between mPF detour g-boundary nodes and mPF cut vertices. Utilizing the notion of maximum mPF spanning trees, we define mPF detour g-boundary nodes and mPF detour g-interior nodes in mPF trees. Additionally, we investigate the characteristics of mPF complete vertices, mPF detour g-interior nodes, and mPF detour g-boundary nodes. Finally, we provide applications of these concepts.