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)

A proper edge-coloring of a graph defines at each vertex the set of colors of its incident edges. This set is called the palette of the vertex. In this paper we are interested in the minimum numberâ€¦ (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)

Let c : E(G)â†’ [k] be a colouring, not necessarily proper, of edges of a graph G. For a vertex v âˆˆ V , let c(v) = (a1, . . . , ak), where ai = |{u : uv âˆˆ E(G), c(uv) = i}|, for i âˆˆ [k]. If we re-orderâ€¦ (More)

A graph G of order n is called arbitrarily partitionable (AP for short) if, for every sequence (n1, . . . , nk) of positive integers with n1 + Â· Â· Â· + nk = n, there exists a partition (V1, . . . ,â€¦ (More)