English

Modular Irregularity Strength of Triangular Book Graph

Combinatorics 2021-11-29 v1 Discrete Mathematics

Abstract

This paper deals with the modular irregularity strength of a graph of n vertices, a new graph invariant, modified from the irregularity strength, by changing the condition of the vertex-weight set associate to the well-known irregular labeling from n distinct positive integer to Z_n-the group of integer modulo n. Investigating the triangular book graph B_m^((3)), we first find the irregularity strength of triangular book graph s(B_m^((3)) ), as the lower bound for the modular irregularity strength, and then construct a modular irregular s(B_m^((3)) )-labeling. The result shows that triangular book graphs admit a modular irregular labeling and its modular irregularity strength and irregularity strength are equal, except for a small case and the infinity property.

Cite

@article{arxiv.2111.12897,
  title  = {Modular Irregularity Strength of Triangular Book Graph},
  author = {Meilin Imelda Tilukay},
  journal= {arXiv preprint arXiv:2111.12897},
  year   = {2021}
}
R2 v1 2026-06-24T07:51:38.335Z