The Reflexive H-Strength on Some Graphs

Abstract

Let G be a connected, simple, and undirected graph with a vertex set V(G) and an edge set E(G). The irregular reflexive -labeling is defined by the function and such that if and if , where max . The irregular reflexive labeling is called an -irregular reflexive -labeling of the graph if every two different sub graphs and isomorphic to it holds , where for the sub graph . The minimum for graph which has an -irregular reflexive -labelling is called the reflexive strength of the graph and denoted by . In this paper we determine the lower bound of the reflexive strength of some subgraphs, on , the sub graph on the sub graph on and the sub graph on .

Keywords

• h irregular reflexive k-labeling
• reflexive h-strength
• path
• wheel
• double fan
• triangular ladder
• ladder graph.