We consider a proper coloring c of edges and vertices in a simple graph and the sum f (v) of colors of all the edges incident to v and the color of a vertex v. We say that a coloring c distinguishesâ€¦ (More)

A 2-packing of a hypergraph H is a permutation Ïƒ on V (H) such that if an edge e belongs to E(H), then Ïƒ(e) does not belong to E(H). We prove that a hypergraph which does not contain neither emptyâ€¦ (More)

We investigate the distinguishing index Dâ€²(G) of a graph G as the least number d such that G has an edge-colouring with d colours that is only preserved by the trivial automorphism. This is an analogâ€¦ (More)

The distinguishing index Dâ€²(G) of a graph G is the least cardinal d such that G has an edge colouring with d colours that is only preserved by the trivial automorphism. This is similar to the notionâ€¦ (More)

An embedding of a simple graph G into its complement G is a permutation Ïƒ on V (G) such that if an edge xy belongs to E(G), then Ïƒ(x)Ïƒ(y) does not belong to E(G). In this note we consider theâ€¦ (More)

We introduce the endomorphism distinguishing number De(G) of a graph G as the least cardinal d such that G has a vertex coloring with d colors that is only preserved by the trivial endomorphism. Thisâ€¦ (More)

In this paper, we show that if the number of arcs in an oriented graph âˆ’â†’ G (of order n) without directed cycles is sufficiently small (not greater than 2 3 nâˆ’ 1), then there exist arc disjointâ€¦ (More)