• Nilesh Kumar

This paper is concerned with the solvability of inequalities or directed graphs G(X) and G2(X) such that G1(X)  G2(X). Graph inequalities have been studied survey papers dating back to the late 1970s by Capobianco (1979) and Cvetković and Smile (1977, 1979). The equalities and inequalities considered in these papers are more general in that they allow arbitrary operations on graphs such as complementation, tensor products, and squaring. In this paper we will show that the solvability of graph inequalities, i.e., having only one graph variable with one specified vertex, is decidable. This will follow from an (exponential) upper bound on the size of a minimal solution (if there is one).

solvability of inequalities, Minimality, graph inequality, nondeterministic exponential time.

"THE SOLVABILITY OF GRAPH INEQUALITIES OVER DIRECTED GRAPHS ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 7, page no.1123-1126, July-2018, Available :http://www.jetir.org/papers/JETIR180Z054.pdf

"THE SOLVABILITY OF GRAPH INEQUALITIES OVER DIRECTED GRAPHS ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 7, page no. pp1123-1126, July-2018, Available at : http://www.jetir.org/papers/JETIR180Z054.pdf