Coloração de arestas distinta na vizinhança

Abstract

An edge coloring is an assignment of colors to the edges of a graph G such that edges that are incident to the same vertex receive distinct colors. Given an edge coloring of a graph G, the color-set of a vertex V is the set of colors on the edges incident to V. Two vertices are distinguishable if their color-sets are different. An adjacent vertex distinguishing (AVD) edge-coloring is an edge coloring such that any two adjacent vertices are distinguishable. The adjacent vertex distinguishing chromatic index of a graph G, denoted by X'a(G), is the least number of colors needed for an AVD-edge coloring of G. This work determines the adjacent vertex distinguishing index for complete tripartite graphs.