A super edge-magic labeling of a graph G = (V, E) of order p and size q is a bijection f : V ∪E → {i} i=1 such that (1) f(u)+ f(uv)+ f(v) = k ∀uv ∈ E and (2) f(V ) = {i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv ∈ E(G), u′, v′ ∈ V (G) and dG(u, u′) = dG(v, v′) < +∞, then f(u) + f(v) = f(u′) + f(v′). I...

In this paper some new results on the acyclic-edge coloring , f -edge coloring, g-edge cover coloring, (g, f )-coloring and equitable edge-coloring of graphs are introduced. In particular, some new results related to the above colorings obtained by us are given. Some new problems and conjectures are presented.

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a(G). It was conjectured by Alon, Sudakov and Zaks (and earlier by Fiamcik) that a(G) ≤ ∆ + 2, where ∆ = ∆(G) denotes the maximum degree of the graph. A...

We prove that, the acyclic chromatic index a′(G) ≤ 6∆ for all graphs with girth at least 9. We extend the same method to obtain a bound of 4.52∆ with the girth requirement g ≥ 220. We also obtain a relationship between g and a′(G).

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a′(G). A graph is called 2-degenerate if any of its induced subgraph has a vertex of degree at most 2. The class of 2-degenerate graphs properly contain...