A proper edge coloring of a graph is adjacent vertex distinguishing if no two adjacent
vertices see the same set of colors. Using a clever application of the local lemma, Hatami J …

An adjacent vertex distinguishing edge coloring is a proper edge coloring such that any two
adjacent vertices have distinct sets consisting of colors of their incident edges. It was …

The irregularity strength of a graph G, s (G), is the least k admitting a {1, 2,…, k}‐weighting of
the edges of G assuring distinct weighted degrees of all vertices, or equivalently the least …

A neighbor sum distinguishing edge-k-coloring, or nsd-k-coloring for short, of a graph G is a
proper edge coloring of G with elements from {1, 2,…, k} such that no pair of adjacent …

The irregularity strength of a graph G, s (G), is the least k such that there exists a {1, 2,…, k}-
weighting of the edges of G attributing distinct weighted degrees to all vertices, or …

Let G be a simple graph. Assume that c is a map** from the edges of G to the set {1, 2,…,
k}. We say that c is neighbor sum distinguishing if every pair of vertex sums of adjacent …

Abstract Let G=(V, E) be a simple graph and ϕ: E (G)→{1, 2,…, k} be a proper k-edge
coloring of G. We say that ϕ is neighbor sum (set) distinguishing if for each edge uv∈ E (G) …

A proper edge k-colouring of a graph G=(V, E) G=(V, E) is an assignment c: E → {1, 2, ..., k\}
c: E→ 1, 2,…, k of colours to the edges of the graph such that no two adjacent edges are …

We consider proper edge colorings of a graph G using colors of the set {1,…, k}. Such a
coloring is called neighbor sum distinguishing if for any uv∈ E (G), the sum of colors of the …

The least k admitting a proper edge colouring c: E→{1, 2,…, k} of a graph G=(V, E) without
isolated edges such that∑ e∋ uc (e)≠∑ e∋ vc (e) for every uv∈ E is denoted by χ Σ′(G) …