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Locally Symmetric Graphs of Girth 4
Author(s) -
Perles Micha A.,
Martini Horst,
Kupitz Yaakov S.
Publication year - 2013
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.21657
Subject(s) - mathematics , combinatorics , odd graph , triangle free graph , bipartite graph , girth (graph theory) , isomorphism (crystallography) , discrete mathematics , 1 planar graph , graph , chordal graph , crystal structure , crystallography , chemistry
We classify the family of connected, locally symmetric graphs of girth 4 (finite and infinite). They are all regular, with the exception of the complete bipartite graphK m , n( 2 ≤ m < n ) . There are, up to isomorphism, exactly four such k ‐regular graphs for every 4 ≤ k < ∞ , one for k = 2 , two for k = 3 , and exactly three for every infinite cardinal k . In the last paragraph, we consider locally symmetric graphs of girth >4.