Adjacent vertex distinguishing edge-colorings and total-colorings of the lexicographic product of 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

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 graphs

We consider lower bounds on the the vertex-distinguishing edge chromatic number of graphs and prove that these are compatible with a conjecture of Burris and Schelp [8]. We also find upper bounds on this number for certain regular graphs G of low degree and hence verify the conjecture for a reasonably large class of such graphs.

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.