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Linear Diophantine Labelling of Graphs

A graph labelling in which the vertices of a finite simple graph on n vertices receive the labels 1..n bijectively and every edge's two endpoint labels have a greatest common divisor that divides n; the resulting linear Diophantine graphs generalize prime graphs, and the topic covers their maximal members together with formulas for their edge counts and vertex degrees.

Dr. Theopolis Text

2501.00640

A linear Diophantine labelling of a finite simple graph on n vertices is a bijection from the vertices to {1, 2, ..., n} such that for every edge the greatest common divisor of its two endpoint label…