Abstract: Brualdi and Massey defined incidence coloring while studying the strong edge chromatic index of bipartite graphs. An incidence of an undirected graph G is a pair $(v,e)$ where $v$ is a vertex of $G$ and $e$ an edge of $G$ incident with $v$. Two incidences $(v,e)$ and $(w,f)$ are adjacent if one of the following holds: (i) $v = w$, (ii) $e = f$ or (iii) $vw = e$ or $f$. An incidence coloring of $G$ assigns a color to each incidence of $G$ in such a way that adjacent incidences get distinct colors. In this talk we present bounds for incidence chromatic number of graphs having high maximum average degree. In particular we prove that every graph with maximum degree at least $7$ and with maximum average degree strictly less than $4$ admits a $(\Delta+3)$-incidence coloring. This result implies that every triangle free planar graph with maximum degree at least $7$ is $(\Delta+3)$-incidence colorable. We will also introduce a similar concept for digraphs and define the oriented incidence chromatic number. Using digraph homomorphism, we show that the oriented incidence chromatic number of a digraph is closely related to the chromatic number of the underlying simple graph. This motivates our study of the oriented incidence chromatic number of symmetric complete digraphs. We give upper and lower bounds for the oriented incidence chromatic number of these graphs, as well as digraphs arising from common graph constructions and decompositions.