2017/06/20 by Daniele Bartoli, Bartoli, Daniele, Tamás Héger +6
Computer Science · Engineering · Mathematics · #05B25 #05C12 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1706.06583
openalex publication_date 2017/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper the metric dimension of (the incidence graphs of) particular\npartial linear spaces is considered. We prove that the metric dimension of an\naffine plane of order q\≥13 is 3q-4 and describe all resolving sets of\nthat size if q\≥ 23. The metric dimension of a biaffine plane (also called\na flag-type elliptic semiplane) of order q\≥ 4 is shown to fall between\n2q-2 and 3q-6, while for Desarguesian biaffine planes the lower bound is\nimproved to 8q/3-7 under q\≥ 7, and to 3q-9\√(q) under certain\nstronger restrictions on q. We determine the metric dimension of generalized\nquadrangles of order (s,1), s arbitrary. We derive that the metric\ndimension of generalized quadrangles of order (q,q), q\≥2, is at least\n\max 6q-27,4q-7 , while for the classical generalized quadrangles W(q)\nand Q(4,q) it is at most 8q.\n