## Abstract

Consider a graph G with a nonempty set of vertices V(G) and a set of edges E(G). Let Z_{n} represent the group of integers modulo n, and let k be a positive integer. A modular irregular labeling of a graph G with order n is a labeling of its edges, ϕ : E(G) → {1,2,...,k}, such that a weight function σ : V(G) → Z_{n} is induced. The weight function is defined as follows: σ(v) = ∑_{u}∈N(v_{)} ϕ(uv) for all vertices v in V(G), where the summation is taken over all vertices u that adjacent with vertex v in G, and this weight function σ must be bijective. The minimum value of k such that a labeling exists in a graph G is called the modular irregularity strength of G, denoted as ms(G). In this research, we have determined the exact values of the modular irregularity strength for generalized book graphs.

Original language | English |
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Article number | 020005 |

Journal | AIP Conference Proceedings |

Volume | 3176 |

Issue number | 1 |

DOIs | |

Publication status | Published - 30 Jul 2024 |

Event | 7th International Conference of Combinatorics, Graph Theory, and Network Topology, ICCGANT 2023 - Hybrid, Jember, Indonesia Duration: 21 Nov 2023 → 22 Nov 2023 |