Let f be a function which assigns a positive integer f(v) to each vertex v

V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v

V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by

(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G)

E(G) to the color set C = {0, 1,

; k - 1} such that |c(

) - c(

)|

r for every two adjacent vertices

and

, |c(

- c(

)|

s and

f(

) for all

V (G),

C where

denotes the number of

-edges incident with the vertex

and

,

are edges which are incident with

but colored with different colors, |c(

)-c(

)|

t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by

(G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.