摘要：The main purpose of the current work is to create new directions for gaining knowledge in the arena of graph labeling. Graph labeling is helpful to assign values (labels), with some conditions to the vertex set or edge set or both. A new graph labeling technique, namely relatively prime edge labeling, is presented in this study. In prime labeling, adjacent vertices receive relatively prime labels, whereas in relatively prime edge labeling edges are labeled in such a manner that adjacent edges receive relatively prime labels. A graph is a relatively prime edge-labeled graph if it admits relatively prime edge labeling. Also, the relatively prime edge labeling is discussed for graphs with vertex or edge duplications. Relatively prime edge labeling for some trees like centipede tree, X-tree, and Y-tree are determined using algorithms in this work. Finally, a relatively prime index number is defined for the graph which fails to be a relatively prime edge-labeled graph.
关键词：Centipede tree;Duplication of graph elements;Prime graph;Relatively prime edge labeling;Relatively prime index
