## Abstract

A total k-labeling is defined as a function g from the edge set to the first natural number k_{e} and a function f from the vertex set to a non-negative even number up to 2k_{v}, where k = max{k_{e}, 2k_{v} }. A vertex irregular reflexive k-labeling of the graph G is total k-labeling if wt(x) ¹ wt(x¢) for every two different vertices x and x¢ of G, where wt(x) = f (x) + Σ _{xy}_{∈E(G)} g(xy). The reflexive vertex strength of the graph G, denoted by rvs(G), is the minimum k for a graph G with a vertex irregular reflexive k-labeling. We will determine the exact value of rvs(G) in this paper, where G is a regular and regular-like graph. A regular graph is a graph where each vertex has the same number of neighbors. A regular graph with all vertices of degree r is called an r-regular graph or regular graph of degree r. A regular-like graphs is an almost regular graph that we develop in a new definition and we called it with (s, r) -almost regular graphs.

Original language | English |
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Pages (from-to) | 1457-1473 |

Number of pages | 17 |

Journal | Journal of Discrete Mathematical Sciences and Cryptography |

Volume | 25 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2022 |

## Keywords

- 05C78
- Almost regular graph
- Irregular reflexive k-labeling
- Reflexive vertex strength
- Regular graph
- Regular-like graph