On The Vertex-distinguishing Edge Coloring And Adjacent Strong Edge Coloring Of Join-graph And Double Graph Of Some Graphs

A normal edge coloring is called vertex-distinguishing coloring .If colored sets from every two vertices incident edge are different, The minimum number of coloring is called vertex-distinguishing edge chromatic number. A vertex-distinguishing edge coloring is called equitable, if the number of edges in any two color classes is less than one, in this case the minimum number of colors is called vertex-distinguishing-equitable edge chromatic number.In this paper, we will give vertex-distinguishing edge chromatic numbers of S_m∨F_n and S_m∨W_n . If n≥2,thasIf n≥3, we will obtainWe discass the vertex-distinguishing-equitable edge chromatic numbers of double graphs of star, and numbers of the fan and the wheel,and get the conclusion.A normal edge coloring is called adjacent strong edge coloring, if colored sets from every two adjacent vertices incident edge are different, and the minimum number of colors is called adjacent strong edge chromatic number. An adjacent strong edge coloring is called equitable adjacent strong edge coloring,if the number of edges in any two color classes is less than one, we call the minimum number of colors as equitable adjacent strong edge chromatic number.In this paper, we also get the adjacent strong edge chromatic numbers of P_m∨F_n and D(P_n). If m≥2,n≥2, we knowIn conclasion equitable adjacent strong edge chromatic numbers of double graphs of star, numbers of the fan and wheel are obtained.