| Autor: |
Kronenthal, Brian G., Miller, Joe, Nash, Alex, Roeder, Jacob, Samamah, Hani, Wong, Tony W. H. |
| Předmět: |
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| Zdroj: |
Journal of Graph Theory; Jan2025, Vol. 108 Issue 1, p50-64, 15p |
| Abstrakt: |
For f:R2→R, let ΓR(f) be a two‐dimensional algebraically defined graph, that is, a bipartite graph where each partite set is a copy of R2 and two vertices (a,a2) and [x,x2] are adjacent if and only if a2+x2=f(a,x). It is known that ΓR(XY) has girth 6 and can be extended to the point‐line incidence graph of the classical real projective plane. However, it was unknown whether there exists f∈R[X,Y] such that ΓR(f) has girth 6 and is nonisomorphic to ΓR(XY). This paper answers this question affirmatively and thus provides a construction of a nonclassical real projective plane. This paper also studies the diameter and girth of ΓR(f) for families of bivariate functions f. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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