Adjacent Strong Edge Coloring Of Special Graph And Classifications Of Special Regular Spanning Subgraphs

Let graph G is a bipartite graph with vertex classes ( X , Y )and| X |＝m,| Y |＝n .if any Vertice's degree of X is k₁ and any vertice's degree of Y is k₂, then G is ( k₁ ,k₂) regular spanning graph.For a graph G (V , E ), if a proper k-edge coloring f is satisfied with C (u )≠C ( v)for uv∈E ( G), Where C (u ) = { f (u v )| uv∈E}, then f is called k-adjacengt strong edge coloring of G, is abbreviated k-ASEC, and X'_as (G)= min{k|k-ASEC of G} is called the adjacent strong edge chromatic number of G.In this paper, ( k₁ ,k₂)regular spanning subgraphs of complete bigraph k m, nare discussed and we consider the problem of complete 3-partite graph G=k_1.m.n(1≤ι≤m≤n )'s adjacent strong edge coloring when 1≤ι≤3. ( k₁ ,k₂). Regular spanning subgraphs of complete bigraph k m, nare discussed and all classifications of ( k₁ ,k₂)regular spanning subgraph about k_{m, n} are given. We consider the problem of complete 3-partite graph G=k_1.m.n(1≤ι≤m≤n )'s adjacent strong edge coloring when 1≤ι≤3, and prove thatâ–³(G)≤X'_as (G)â–³(G)+2when 1≤ι≤3, we have a conjecture forι≥4 .