STAR CHROMATIC INDEX OF LINE GRAPHS OF THE FAMILY OF LADDER GRAPHS

Abstract

   A star edge coloring of a graph  is a proper edge-coloring without bichromatic paths or cycles of length 4. The smallest integer k such that  admits a star-edge-coloring with  colors is the star chromatic index of  and is denoted by The Line Graph  of a graph  is the one in which  corresponds to the edges of  and two vertices of   are   adjacent if and only if their corresponding edges in  meet at a common vertex in  . In this paper, we obtain the star chromatic index of the line graph of the ladder graphs, triangular ladder graphs and diagonal ladder graphs.