Note on edge irregular reflexive labelings of graphs

Abstract

For a graph , an edge labeling and a vertex labeling are called total -labeling, where . The total -labeling is called an edge irregular reflexive -labeling of the graph , if for every two different edges and of , one has The minimum for which the graph has an edge irregular reflexive -labeling is called the reflexive edge strength of . In this paper we determine the exact value of the reflexive edge strength for cycles, Cartesian product of two cycles and for join graphs of the path and cycle with .

Keywords

• edge irregular reflexive labeling
• reflexive edge strength
• cycles
• cartesian product of cycles