VERTEX INDUCED k-EDGE COLORING AND VERTEX INCIDENT k-EDGE COLORING OF GRAPHS

Let k & GE; 2 be a natural number. Then the vertex induced k-edge coloring number & psi;& PRIME;vik(G) of a simple connected graph G = (V, E) is the highest number of colors needed to color the edges of a graph G such that the edges of the subgraph induced by the closed neighborhood N[v] of the vertex v & ISIN; V(G) receives not more than k colors.The vertex incident k-edge coloring number & psi;& PRIME;vink(G) of a simple connected graph G = (V, E) is the highest number of colors required to color the edges of a graph G such that the edges incident to a vertex v in graph G receives not more than k colors. In this paper, we initiate the study on & psi;& PRIME;vik(G) and & psi;& PRIME;vink(G). We also determine the exact values of & psi;& PRIME;vik(G) and & psi;& PRIME;vink(G) for k = 2 for some special graphs.