The partition of indeterminacy function the neutrosophic set into contradiction part and ignorance represent quadripartitioned single valued set. In this work, new concept bipolar graph is established, operations on it are studied. Cartesian product, cross lexicographic strong product composition investigated. proposed concepts illustrated with examples.

Let G1 ⊗ G2 be the strong product of a k-extendable graph G1 and an l-extendable graph G2, and X an arbitrary set of vertices of G1⊗G2 with cardinality 2[(k + 1)(l + 1)/2]. We show that G1 ⊗ G2 − X contains a perfect matching. It implies that G1 ⊗ G2 is [(k + 1)(l + 1)/2]-extendable, whereas the Cartesian product of G1 and G2 is only (k+l+1)extendable. As in the case of the Cartesian product, t...

A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of chordal and circular arc graphs. Even though 1-p.o. graphs can be recognized in polynomial time, no structural characterization of 1-p.o. graphs is known. In this ...