Let c be a proper edge coloring of a graph with integers. Then, while Vizing's theorem
guarantees that we can take. On the course of investigating irregularities in graphs, it has …

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 …

The adjacent vertex distinguishing edge coloring of a graph G is a proper edge coloring in
which each pair of adjacent vertices is assigned different color sets. The smallest number of …

Let GG be a simple graph with no isolated edges. The neighbor-distinguishing edge
coloring of GG is a proper edge coloring of GG such that any pair of adjacent vertices have …

The adjacent vertex-distinguishing chromatic index χ'_ avd (G) χ avd′(G) of a graph GG is
the smallest integer kk for which GG admits a proper edge k k-coloring such that no pair of …

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 …

Symmetry, such as structural symmetry, color symmetry and so on, plays an important role in
graph coloring. In this paper, we use structural symmetry and color symmetry to study the …

Context. In the last decades, the importance of computer science grew in the everyday life. In
the same time, theoretical aspects of computer science have been developed, and in …

A proper vertex k-coloring of a graph G=(V, E) is an assignment c: V→{1, 2,…, k} of colors to
the vertices of the graph such that no two adjacent vertices are associated with the same …

In this paper, we consider the adjacent vertex distinguishing proper edge coloring (for short,
AVDPEC) and the adjacent vertex distinguishing total coloring (for short, AVDTC) of a fuzzy …