Family of Ladder Graphs are Properly Lucky

The proper labeling is different natural number for adjacent nodes. Lucky labeling is that the total of labels over adjacent nodes within the graph is not same. Lucky labeling is linked with proper labeling. The aim of the paper is to show proper lucky labeling and proper lucky number of a ladder graph, open ladder graph, slanting ladder graph, triangular ladder graph, open triangular graph, diagonal ladder graph and open diagonal ladder graph.