Diophantine Graphs
Combinatorics
2026-01-01 v2 Number Theory
Abstract
This manuscript introduces Diophantine labeling, a new way of labeling of the vertices for finite simple undirected graphs with some divisibility condition on the edges. Maximal graphs admitting Diophantine labeling are investigated and their number of edges are computed. Some number-theoretic techniques are used to characterize vertices of maximum degree and nonadjacent vertices. Some necessary and sufficient conditions for vertices of equal degrees are found.
Cite
@article{arxiv.2501.00640,
title = {Diophantine Graphs},
author = {A. Nasr and A. Elsonbaty and M. A. Seoud and M. Anwar},
journal= {arXiv preprint arXiv:2501.00640},
year = {2026}
}