let $g$ be a simple graph of order $n$‎. ‎we consider the‎ ‎independence polynomial and the domination polynomial of a graph‎ ‎$g$‎. ‎the value of a graph polynomial at a specific point can give‎ ‎sometimes a very surprising information about the structure of the‎ ‎graph‎. ‎in this paper we investigate independence and domination‎ ‎polynomial at $-1$ and $1$‎.

We consider the problem of compression for “easy” Boolean functions: given the truth table of an n-variate Boolean function f computable by some unknown small circuit from a known class of circuits, find in deterministic time poly(2) a circuit C (no restriction on the type of C) computing f so that the size of C is less than the trivial circuit size 2/n. We get both positive and negative result...

The concept of Morgan tree [6] is shown to be useful in generation of all nonisomorphic trees. Namely, to each tree one can assign canonical Morgan tree. Since, the number of Morgan trees [5, 1] is much larger then number of canonical Morgan trees, it is of interest to create an efficient algorithm that creates only a fraction of Morgan trees not eliminating the single canonical Morgan tree. Th...