The Endomorphism Type of Certain Bipartite Graphs and a Characterization of Projective Planes
نویسندگان
چکیده
In [2] Fan 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 < g ≤ 2d, and (2) every pair of adjacent edges is contained in a circuit of length g.
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 29 شماره
صفحات -
تاریخ انتشار 2013