Adjacent Vertex Distinguishing Edge-colorings of the Lexicographic Product of Special Graphs

Adjacent Vertex Distinguishing Edge-Colorings

An adjacent vertex distinguishing edge-coloring of a simple graph G is a proper edge-coloring of G such that no pair of adjacent vertices meets the same set of colors. The minimum number of colors χa(G) required to give G an adjacent vertex distinguishing coloring is studied for graphs with no isolated edge. We prove χa(G) ≤ 5 for such graphs with maximum degree Δ(G) = 3 and prove χa(G) ≤ Δ(G) ...

Adjacent vertex distinguishing edge-colorings of meshes

adjacent vertex distinguishing acyclic edge coloring of the cartesian product of graphs

‎let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$‎. ‎we also determine‎ ‎exact value of this parameter for the cartesian product of ...

Gap vertex-distinguishing edge colorings of graphs

In this paper, we study a new coloring parameter of graphs called the gap vertexdistinguishing edge coloring. It consists in an edge-coloring of a graph G which induces a vertex distinguishing labeling of G such that the label of each vertex is given by the difference between the highest and the lowest colors of its adjacent edges. The minimum number of colors required for a gap vertex-distingu...

Vertex-distinguishing edge colorings of random graphs

A proper edge coloring of a simple graph G is called vertex-distinguishing if no two distinct vertices are incident to the same set of colors. We prove that the minimum number of colors required for a vertex-distinguishing coloring of a random graph of order n is almost always equal to the maximum degree ∆(G) of the graph.