(3,1) – total labeling of cycle, path graphs and some related graphs

Abstract

The (3,1)- total labeling of a graph G is an assignment of non- negative integers to vertices and edges of G such that no two adjacent vertices or edges have the same label and the difference of labels between a vertex and its incident edges is at least 3. In this paper, we study the (3,1)- total labeling for some types of graphs and derive their (3,1)- total labeling number.