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Locally 4‐by‐4 grid graphs
Author(s) -
Blokhuis A.,
Brouwer A. E.
Publication year - 1989
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190130209
Subject(s) - mathematics , combinatorics , grid , indifference graph , chordal graph , 1 planar graph , maximal independent set , metric dimension , discrete mathematics , pathwidth , graph , line graph , geometry
We investigate locally grid graphs. The main results are (i) a characterization of the Johnson graphs (and certain quotients of these) as locally grid graphs such that two points at distance 2 have precisely four common neighbors, and (ii) a complete determination of all graphs that are locally a 4 × 4 grid (it turns out that there are four such graphs, with 35, 40, 40, and 70 vertices).