A graph is locally irregular if no two adjacent vertices have the same degree. The irregular
chromatic index χ irr′(G) of a graph G is the smallest number of locally irregular subgraphs …

A graph is locally irregular if the neighbors of every vertex v have degrees distinct from the
degree of v. A locally irregular edge-coloring of a graph G is an (improper) edge-coloring …

A locally irregular graph is a graph in which the end vertices of every edge have distinct
degrees. A locally irregular edge coloring of a graph G is any edge coloring of G such that …

A graph G is said to be locally irregular if each pair of adjacent vertices have different
degrees in G. A collection of edge disjoint subgraphs (G 1,…, G k) of G is called a k-locally …

A graph is locally irregular if the degrees of the end-vertices of every edge are distinct. An
edge coloring of a graph G is locally irregular if every color induces a locally irregular …

A graph is locally irregular if any pair of adjacent vertices have distinct degrees. A locally
irregular decomposition of a graph G is a decomposition D of G such that every subgraph …

A graph in which the two end-vertices of every edge have distinct degrees is called locally
irregular. An edge coloring of a graph G such that every color induces a locally irregular …

A (undirected) graph is locally irregular if no two of its adjacent vertices have the same
degree. A decomposition of a graph G into k locally irregular subgraphs is a partition …

A graph is locally irregular if no two adjacent vertices have the same degree. A locally
irregular edge-coloring of a graph G is such an (improper) edge-coloring that the edges of …

The current work is mainly related to the well-known 1-2-3 Conjecture, which is defined
accordingly to the upcoming notions. Let G be a graph, and let ω be an edge-weighting …