Injective Edge Coloring of Cubic Graphs

Abstract

Three edges e1, e2 and e3 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 e1, e2, e3 are consecutive, then e1 and e3 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.