Locally Symmetric Graphs of Girth 4 | Zendy

Perles Micha A. | Zendy; Martini Horst | Zendy; Kupitz Yaakov S. | Zendy

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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.

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