An antimagic labeling of a graph G is bijection f:E(G)?{1,…,|E(G)|} such that the weights w(x)=?y?xf(y) distinguish all vertices. A well-known conjecture Hartsfield and Ringel (1990) every connected other than K2 admits an labeling. For set distances D, D-antimagic f:V(G)?{1,…,|V(G)|} weight?(x)=?y?ND(x)f(y) distinct for each vertex x, where ND(x)={y?V(G)|d(x,y)?D} D-neigbourhood x. If ND(x)=r,...

Abstract We discuss a new memory-efficient depth-first algorithm and its implementation that iterates over all elements of finite locally branched lattice. This can be applied to face lattices polyhedra various generalizations such as polyhedral complexes subdivisions manifolds, extended tight spans closed sets matroids. Its practical is very fast compared state-of-the-art implementations previ...

The present work aims to exploit the interplay between algebraic properties of rings and graph-theoretic structures some associated graphs. We introduce commutatively closed graphs investigate subsets a ring with help graph theory. In particular, we compute diameter matrix Artinian semisimple algebras.

The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case ...

in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.