## Abstract

Let G be a connected, simple, and undirected graph with a vertex set V(G) and an edge set E(G). Total k-labeling is a function f_{e} from the edge set to the first k_{e} natural number, and a function f_{v} from the vertex set to the non negative even number up to 2k_{v}, where k = max k_{e}, 2k_{v} }. An edge irregular reflexive k labeling of the graph G is the total k-labeling, if for every two different edges x _{1} x _{2} and x_{1}' x_{2}' of G,wt(x_{1} x_{2} ≠ wt(x_{1}' x_{2}' where wt(x_{1} x_{2} =f_{v} x_{1} +f_{e} x_{1} x_{2} + f_{v}(x_{2}). The minimum k for graph G which has an edge irregular reflexive k-labelling is called the reflexive edge strength of the graph G, denoted by res(G). In this paper, we determined the exact value of the reflexive edge strength of family trees, namely generalized sub-divided star graph, broom graphs, and double star graph.

Original language | English |
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Article number | 012008 |

Journal | Journal of Physics: Conference Series |

Volume | 1543 |

Issue number | 1 |

DOIs | |

Publication status | Published - 29 May 2020 |

Event | 3rd International Conference on Current Scenario in Pure and Applied Mathematics, ICCSPAM 2020 - Tamil Nadu, India Duration: 30 Jan 2020 → 31 Jan 2020 |

## Keywords

- Edge irregular reexive labeling
- broom graph
- double star graph
- generalized sub-divided star graph
- reexive edge strength