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 G without isolated edges is neighbor‐distinguishing if any
two adjacent vertices have distinct sets consisting of colors of their incident edges. The …

A proper edge coloring of a graph G is neighbor-distinguishing if any two adjacent vertices
have distinct sets consisting of colors of their incident edges. The neighbor-distinguishing …

An adjacent vertex-distinguishing edge coloring (AVD-coloring) of a graph is a proper edge
coloring such that no two neighbors are adjacent to the same set of colors. Zhang et al.[17] …

An adjacent vertex distinguishing coloring of a graph G is a proper edge coloring of G such
that any pair of adjacent vertices are incident with distinct sets of colors. The minimum …

An adjacent vertex distinguishing proper edge coloring of a graph G is a proper edge
coloring of G such that no pair of adjacent vertices meets the same set of colors. Let χ′ a …

An adjacent vertex distinguishing edge coloring of a graph G is a proper edge coloring of G
such that any pair of adjacent vertices admit different sets of colors. The minimum number of …

An adjacent vertex distinguishing coloring of a graph G is a proper edge coloring of G such
that any pair of adjacent vertices admits different sets of colors. The minimum number of …

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 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 …