We present a novel approach to solve quantified boolean formulas with one quantifier alternation (2QBF). The algorithm incrementally adds new constraints to the formula until the constraints describe a unique Skolem function or until the absence of a Skolem function is detected. Backtracking is required if the absence of Skolem functions depends on the newly introduced constraints. We present t...

Let D = (V, A)be a digraph. An injective function f: V(D) → {1,2, .... p} is said to be sign pairity difference cordial labeling if the induced arc f∗: A(D) {0,1} defined byf∗ ((μ, ν)) satisfiesthe condition that |ef 0-ef(1)| ≤ 1 where, ef(0) number of arcs with label 0 and ef(1) 1. In this paper, we analyze existence in digraphs Directed Path , Cycle, Outstar, Inwheel Downcomb by K.Palani et.al.

Every integer is either even or odd, so we know that the polynomial f(x) = x(x− 1) 2 is integervalued on the integers, even though its coefficients are not in Z. Similarly, since every binomial coefficient ( k n ) is an integer, the polynomial ( x n ) = x(x− 1)...(x− n+ 1) n! must also be integervalued. These polynomials were used for polynomial interpolation as far back as the 17 century. Inte...

Stochastic Boolean satisfiability (SSAT) is a formalism allowing decision-making for optimization under quantitative constraints. Although SSAT solvers are active development, existing do not provide Skolem-function witnesses, which crucial practical applications. In this work, we develop new witness-generating solver, SharpSSAT, integrates techniques, including component caching, clause learni...

It is known that if an almost bipartite graph G with n edges possesses a γlabeling, then the complete graphK2nx+1 admits a cyclicG-decomposition. We introduce a variation of γ-labeling and show that whenever an almost bipartite graph G admits such a labeling, then there exists a cyclic Gdecomposition of a family of circulant graphs. We also determine which odd length cycles admit the variant la...

Let [n]∗ denote the set of integers {−n−1 2 , . . . , n−1 2 } if n is odd, and {−n 2 , . . . , n 2 } \ {0} if n is even. A super edge-graceful labeling f of a graph G of order p and size q is a bijection f : E(G) → [q]∗, such that the induced vertex labeling f ∗ given by f ∗(u) = ∑ uv E(G) f(uv) is a bijection f ∗ : V (G) → [p]∗. A graph is super edge-graceful if it has a super edge-graceful la...

An assignment of integer numbers to the vertices of a given graph under certain conditions is referred to as a graph labeling. The assignment of labels from the set {0,1,2,...,2 1} q to the vertices of G (with ( ) G n V vertices and ( ) q E G edges) such that, when each edge has assigned a label defined by the absolute difference of its end-points, the resulting edge labels are 1,3 ,2 1 q is re...