The Vertex-Distinguishing Edge Coloring of 𝑷𝒎⋁𝑲𝒏 and 𝑪𝒎 ∨ 𝑲𝒏

A proper edge coloring of graph G is called equitable adjacent strong edge coloring if colored sets from every two adjacent vertices incident edge are different, and the number of edges in any two color classes differ by at most one, which the required minimum number of colors are called the adjacent strong equitable edge chromatic number. In this paper, we obtain vertex-distinguishing edge coloring of 𝑃𝑚 ∨ 𝐾𝑛 and 𝐶𝑚 ∨ 𝐾𝑛.