Graphs with vertex-coloring and detectable 2-edge-weighting
Nagarajan Paramaguru, R. Sampathkumar · AKCE International Journal of Graphs and Combinatorics · 2016
For a connected graph of order and a -edge-weighting of the edges of , the code, , of a vertex of is the ordered -tuple , where is the number of edges incident with that are weighted . (i) The -edge-weighting is detectable if every two adjacent vertices of have distinct codes. The minimum positive integer for which has a detectable -edge-weighting is the detectable chromatic number of . (ii) The -edge-weighting is a vertex-coloring if every two adjacent vertices of with codes and have . The minimum positive integer for which has a vertex-coloring -edge-weighting is denoted by . In this paper, we have enlarged the known families of graphs with .