1 research outputs found
On sum edge-coloring of regular, bipartite and split graphs
An edge-coloring of a graph with natural numbers is called a sum
edge-coloring if the colors of edges incident to any vertex of are distinct
and the sum of the colors of the edges of is minimum. The edge-chromatic
sum of a graph is the sum of the colors of edges in a sum edge-coloring of
. It is known that the problem of finding the edge-chromatic sum of an
-regular () graph is -complete. In this paper we give a
polynomial time -approximation algorithm for the
edge-chromatic sum problem on -regular graphs for . Also, it is
known that the problem of finding the edge-chromatic sum of bipartite graphs
with maximum degree 3 is -complete. We show that the problem remains
-complete even for some restricted class of bipartite graphs with maximum
degree 3. Finally, we give upper bounds for the edge-chromatic sum of some
split graphs.Comment: 11 page