Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications

Abstract

In this paper, we obtain a characterization of bipolar fuzzy detour $g$-eccentric node. The concepts of bipolar fuzzy detour $g$-boundary nodes and bipolar fuzzy detour $g$-interior nodes in a bipolar fuzzy graph are examined. Also we establish the relationship between bipolar fuzzy cut node and bipolar fuzzy detour $g$-boundary node. Some properties of bipolar fuzzy detour $g$-boundary nodes, bipolar fuzzy detour $g$-interior nodes and bipolar fuzzy complete nodes are discussed. Bipolar fuzzy detour $g$-interior node and bipolar fuzzy detour $g$-boundary node of a bipolar fuzzy tree are introduced using maximum bipolar fuzzy spanning tree. Applications of detour $g$-distance, detour $g$-boundary node, detour $g$-interior node are given.