Journal article

Publication year: 2013

Pages: 253-257

Journal: Graphs and Combinatorics

Volume number: 29

Issue number: 2

ISSN: 0911-0119

eISSN: 1435-5914

DOI Link: https://doi.org/10.1007/s00373-011-1110-6

Publisher: Springer

Abstract: 
Fan (in Southeast Asian Bull Math 25, 217-221, 2001) determines the endomorphism type of a finite projective plane. In this note we show that Fan's result actually characterizes the class of projective planes among the finite bipartite graphs of diameter three. In fact, this will follow from a generalization of Fan's theorem and its converse to all finite bipartite graphs with diameter d and girth g such that (1) d + 1 < ga parts per thousand currency sign2d, and (2) every pair of adjacent edges is contained in a circuit of length g.

Harvard Citation style: Koehl, R., Moeser, K. and Van Maldeghem, H. (2013) The Endomorphism Type of Certain Bipartite Graphs and a Characterization of Projective Planes, Graphs and Combinatorics, 29(2), pp. 253-257. https://doi.org/10.1007/s00373-011-1110-6

APA Citation style: Koehl, R., Moeser, K., & Van Maldeghem, H. (2013). The Endomorphism Type of Certain Bipartite Graphs and a Characterization of Projective Planes. Graphs and Combinatorics. 29(2), 253-257. https://doi.org/10.1007/s00373-011-1110-6