Let = () be a graph without isolated vertices. We say that ⊂ is a if every vertex has a neighbor in . Let () denote the minimum cardinality of a total dominating set of . We prove that if is a graph of order and minimum degree at least 3 then () ≤ /2. If equality holds then must be 3-regular...

Let denote the class of intersection graphs of linear 3-uniform hypergraphs. In this paper a polynomial algorithm solving the recognition problem for the graphs with bound on minimum vertex degree δ()≥ 13 is proposed

This paper deals with the problem of constructing directed trees of optimal weight and root with depth at most (||) (called − ). We first prove that the maximization and the minimization versions are equal-approximable under the that measures how the value of an approximate solution is placed...

This paper deals with the problem of constructing directed trees of optimal weight and root with depth at most (||) (called – ). We first prove that the maximization and the minimization versions are equal-approximable under the that measures how the value of an approximate solution is placed...

A dual-Eulerian graph is a plane graph which has an ordering defined on its edge set which forms simultaneously an Euler circuit in the graph and an Euler circuit in the dual graph. Dual-Eulerian graphs were defined and studied in the context of silicon optimization of cmos layouts. They are...

The possibilities for circuits of length 4 to appear together in a cubic bigraph are classified. That has consequences on the structure of minimally 1-factorable regular bigraphs, i.e. those in which each 1-factor lies in precisely one 1-factorization. We characterize minimally 1-factorable...

We define an between finite simple graphs and use it to define an equivalence relation on the set of natural numbers. The least integers of the equivalence classes serve as canonical code numbers for graphs and this new integer sequence we call the sequence of Characterizations of the...

This paper is about the way to transform any equation into other equations. Moreover, except from that this method allows the transformation of any equation into any other form, there is and the transformation of Cartesian axes into transformed axes. Then, it is plausible with the transformed...

A new approach to the problem is presented. The difficulty of the problem is characterized by the existence of two kinds of chaining processes. A conjecture claiming that the two examined chaining are the only possible is formulated. Should such conjecture be true, the approach could be...