On the total-neighbor-distinguishing index by sums
Presented by Monika PILSNIAK
Type: Oral presentation
Track: Coloring of Graphs
We consider a proper coloring c of edges and vertices in a simple graph and the function f(v) of sum of colors of all the edges incident to v and the color of a vertex v. We say that a coloring c distinguishes adjacent vertices by sums, if every two adjacent vertices have different values of f. We conjecture that \Delta +3 colors suffice to distinguish adjacent vertices in any simple graph. We show that this holds for complete graphs, cycles, bipartite graphs, cubic graphs and graphs with maximum degree at most three.