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A bipolar fuzzy graph is a generalization of graph theory by using bipolar fuzzy sets. The bipolar fuzzy sets are an extension of fuzzy sets. This paper introduces an effective degree of a vertex, a (ordinary) degree of a vertex in bipolar fuzzy graph as analogous of fuzzy graph, a semiregular bipolar fuzzy graph, and a semicomplete bipolar fuzzy graph. Further, this paper gives some propositions. Mathematics Subject Classification: 03E72, 05C07

In this paper, we introduce the concepts of a fuzzy prime and an anti fuzzy prime implicative filter of lattice W-algebras and discuss some of their properties.

This paper introduces the concepts of perfect bipolar fuzzy graph, complete perfect bipolar fuzzy graph, semi-perfect bipolar fuzzy graph, and further investigates some of their properties.

Abstract:A graph consists of a nonempty vertex set and an edge set, denoted G=(V, E). An unordered pair of edge v,w is known as an undirected edge and an ordered pair of edge (v, w) is known as a directed edge. A graph with directed edges is called a directed graph, simply a digraph; otherwise an undirected graph. Usually, an undirected graph is simply known as a graph. This paper gives a new approach to complete graph and investigates some results related to this idea.