Automorphism properties of embedded graphs | Zendy

Hutchinson Joan P. | Zendy

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Automorphism properties of embedded graphs

Author(s) -

Hutchinson Joan P.

Publication year - 1984

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.3190080105

Subject(s) - mathematics , combinatorics , automorphism , planar graph , vertex (graph theory) , embedding , 1 planar graph , automorphism group , graph , torus , symmetric graph , toroid , face (sociological concept) , genus , discrete mathematics , chordal graph , line graph , geometry , computer science , voltage graph , artificial intelligence , social science , physics , plasma , botany , quantum mechanics , sociology , biology

This paper presents some conditions under which every automorphism of a graph, embedded on a surface of positive genus, maps face boundaries of the embedding to face boundaries. These results extend a result of Whitney which provides an analogous, but simpler, condition for planar graphs. The new result is applied to graphs on the torus to obtain a classification of many toroidal vertex‐, edge‐, and face‐transitive graphs.

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