We consider the problem of computing Skolem functions for satisfied dependency quantified Boolean formulas (DQBFs). We show how Skolem functions can be obtained from an elimination-based DQBF solver and how to take preprocessing steps into account. The size of the Skolem functions is optimized by don’t-care minimization using Craig interpolants and rewriting techniques. Experiments with our DQB...

Let G be a graph with p vertices and q edges an injective function, where k is positive integer. If the induced edge labeling defined by for each bijection, then f called odd Fibonacci irregular of G. A which admits graph. The irregularity strength ofes(G) minimum labeling. In this paper, some subdivision graphs obtained from vertex identification determined.

A labeling f on a graph G on n vertices is called a prime labeling if f is a bijection from the vertex set V (G) to {1, 2, · · · , n} such that f(x) and f(y) are coprime if x and y are adjacent. It was shown by Sundaram et al. [1] that the planar grid Pm × Pn has a prime labeling if m ≤ n and n is a prime. In this paper it is proved that the following grids have a prime labeling: (i) Pn+1 × Pn+...

The Skolem machine is a Turing-complete machine model where the instructions are first-order formulas of a specific form. We introduce Skolem machines and prove their logical correctness and completeness. Skolem machines compute queries for the Geolog language, a rich fragment of first-order logic. The concepts of Geolog trees and complete Geolog trees are defined, and these tree concepts are u...

an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...