Boundary and Interior Nodes in a Fuzzy Graph Using Sum Distance

In this paper, the concepts of boundary nodes and interior ones are introduced in a fuzzy graph based on sum distance with relationship among boundary nodes, interior nodes, fuzzy cutnodes and complete nodes. It is observed that fuzzy cutnodes can be boundary nodes and there are nodes in G, neither boundary nodes nor interior ones. It is verified that a complete node need not be a boundary one and a node which is a boundary one of all other nodes need not be complete. In fuzzy trees, it is observed that fuzzy end nodes need not be boundary ones and vice versa. It is verified that in a complete fuzzy graph there exist at most one node which is not a boundary one. Also boundary nodes of a self centered fuzzy cycle are identified together with interior nodes of a complete fuzzy graph.