Constructing $\{K_{2s},T_{ts,t}\}$-Homogeneous Graphs with Ordered Pencils

Details Constructing $\{K_{2s},T_{ts,t}\}$-Homogeneous Graphs with Ordered Pencils Constructing $\{K_{2s},T_{ts,t}\}$-Homogeneous Graphs with Ordered Pencils

2007-04-17

arxiv.org/abs/0704.2146v20

Mathematics

Combinatorics

15 pages

Scientific paper

Let $\mathcal C$ be a class of graphs.A restricted concept of $\mathcal C$-homogeneous graphs generalizing the $\mathcal C$-ultrahomogeneous graphs of \cite{I} is given. Subsequently, a construction of non-line-graphical $\{K_{2s},T_{ts,t}\}_{K_2}$-homogeneous graphs that includes the $\{K_4,K_{2,2,2}\}_{K_2}$-ultrahomogeneous graph of \cite{Dej2}, by means of ordered pencils of binary projective spaces, is shown to yield 20 such graphs that are not $\{K_{2s},T_{ts,t}\}_{K_2}$-ultrahomogeneous, even though 5 of them still are $\{K_{2s}\}$-ultrahomogeneous for $s=2$, and conjectured to produce an infinity of graphs with similar properties, in terms of configurations of points and lines.

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