Injective Edge Coloring of Cubic Graphs

Three edges e 1 , e 2 and e 3 in a graph G are consecutive if they form a cycle of length 3 or a path in this order. A k -injective edge-coloring of a graph G is an edge-coloring of G , (not necessarily proper), such that if edges e 1 , e 2 , e 3 are consecutive, then e 1 and e 3 receive distinct colors. The minimum k for which G has a k -injective edge-coloring is called the injective edge-coloring number, denoted by χ′ i ( G ). In this paper, injective edge-coloring numbers of H -graph and generalized H -graph are determined.