Adjacent vertex distinguishing index of bipartite planar graphs

Abstract

A proper edge coloring of a graph $G$ is called adjacent vertex distinguishing, if any pair of adjacent vertices meet distinct color sets. The adjacent vertex distinguishing index of $G$, denoted by $\chi_a(G)$, is the smallest integer $k$ such that $G$ has an adjacent vertex distinguishing edge $k$-coloring. In this paper, we show that every bipartite planar graph $G$ with maximum degree $\Delta\ge 7$ and without isolated edges has $\chi_{a