AVD edge-colorings of cubic Halin graphs

Abstract

The adjacent vertex-distinguishing edge-coloring of a graph $ G $ is a proper edge-coloring of $ G $ such that each pair of adjacent vetices receives a distinct set of colors. The minimum number of colors required in an adjacent vertex-distinguishing edge-coloring of $ G $ is called the adjacent vertex-distinguishing chromatic index. In this paper, we determine the adjacent vertex distinguishing chromatic indices of cubic Halin graphs whose characteristic trees are caterpillars.

Keywords

• avd edge-coloring
• adjacent vertex-distinguishing chromatic index
• halin graphs
• cubic graphs